<PAGE>   1
                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
                                  SCHEDULE 13G
 
                   UNDER THE SECURITIES EXCHANGE ACT OF 1934
                               (AMENDMENT NO. 1)*
 
                            Network Appliance, Inc.
- --------------------------------------------------------------------------------
                                (Name of Issuer)
 
                           Common Stock, No Par Value
- --------------------------------------------------------------------------------
                         (Title of Class of Securities)
 
                                  64120L 10 4
- --------------------------------------------------------------------------------
                                 (CUSIP Number)
 
Check the following box if a fee is being paid with this statement / /. (A fee
is not required only if the filing person: (1) has a previous statement on file
reporting beneficial ownership of more than five percent of the class of
securities described in Item 1; and (2) has filed no amendment subsequent
thereto reporting beneficial ownership of five percent or less of such class.)
(See Rule 13d-7.)
 
*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter the
disclosures provided in a prior cover page.
 
The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).
 
                        (Continued on following page(s))
 
                               Page 1 of 4 Pages
 
SEC 1745 (10-88)

<PAGE>   2
 
CUSIP NO. 64120L 10 4                13G                      PAGE 2 OF 4 PAGES
 

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<S> <C>
- --------------------------------------------------------------------------------------------------------------
  1   NAME OF REPORTING PERSON
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
     
      Advent VII L.P.                                                       04-3181563
      Advent Atlantic and Pacific II L.P.                                   04-3123521
      Advent New York L.P.                                                  04-3095408
      Advent Industrial II L.P.                                             51-0314268
      TA Venture Investors Limited Partnership                              04-3068354                        
- --------------------------------------------------------------------------------------------------------------
  2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
 
      (a)  /X/       (b)  / /
- --------------------------------------------------------------------------------------------------------------
  3   SEC USE ONLY
- --------------------------------------------------------------------------------------------------------------
  4   CITIZENSHIP OR PLACE OF ORGANIZATION

      Advent VII L.P.                                                       Delaware
      Advent Atlantic and Pacific II L.P.                                   Delaware
      Advent New York L.P.                                                  Delaware
      Advent Industrial II L.P.                                             Delaware
      TA Venture Investors Limited Partnership                              Massachusetts                     
- --------------------------------------------------------------------------------------------------------------
                     5     SOLE VOTING POWER

                           Advent VII L.P.                                       0
                           Advent Atlantic and Pacific II L.P.                   0 
                           Advent New York L.P.                                  0
                           Advent Industrial II L.P.                             0
                           TA Venture Investors Limited Partnership              0                       
      
                     ------------------------------------------------------------------------------------------
      NUMBER OF      6     SHARED VOTING POWER                                                                 
       SHARES              
    BENEFICIALLY           N/A
      OWNED BY       ------------------------------------------------------------------------------------------
        EACH         7     SOLE DISPOSITIVE POWER                                                              
      REPORTING      
       PERSON              Advent VII L.P.                                       0
        WITH               Advent Atlantic and Pacific II L.P.                   0 
                           Advent New York L.P.                                  0
                           Advent Industrial II L.P.                             0
                           TA Venture Investors Limited Partnership              0               
                     ------------------------------------------------------------------------------------------
                     8     SHARED DISPOSITIVE POWER 

                           N/A
- ---------------------------------------------------------------------------------------------------------------
  9   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

      Advent VII L.P.                                                            0
      Advent Atlantic and Pacific II L.P.                                        0
      Advent New York L.P.                                                       0
      Advent Industrial II L.P.                                                  0 
      TA Venture Investors Limited Partnership                                   0              
- --------------------------------------------------------------------------------------------------------------
 10   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*
- --------------------------------------------------------------------------------------------------------------
 11   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

      Advent VII L.P.                                                         00.0%
      Advent Atlantic and Pacific II L.P.                                     00.0%
      Advent New York L.P.                                                    00.0%
      Advent Industrial II L.P.                                               00.0%
      TA Venture Investors Limited Partnership                                00.0%               
- --------------------------------------------------------------------------------------------------------------
 12   TYPE OF REPORTING PERSON

      Each entity is a Limited Partnership
- --------------------------------------------------------------------------------------------------------------
 
- --------------------------------------------------------------------------------------------------------------
</TABLE>

 
                      *SEE INSTRUCTION BEFORE FILLING OUT!

<PAGE>   3
 
SCHEDULE 13G                                                   Page 3 of 4 Pages
 

<TABLE>
<S>         <C>    <C>
Item 1(a)          NAME OF ISSUER:

                   Network Appliance, Inc.

Item 1(b)          ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES:

                   295 North Bernardo Drive
                   Mountain View, CA 94043
 
Item 2(a)          NAME OF PERSON FILING:

                   Advent VII L.P.                           
                   Advent Atlantic and Pacific II L.P.      
                   Advent New York L.P.                     
                   Advent Industrial II L.P.                
                   TA Venture Investors Limited Partnership 

Item 2(b)          ADDRESS OF PRINCIPAL BUSINESS OFFICE:

                   c/o TA Associates
                   125 High Street, Suite 2500
                   Boston, MA 02110

Item 2(c)          CITIZENSHIP:  Not Applicable
                                 
Item 2(d)          TITLE OF CLASS OF SECURITIES: Common Stock, No Par Value

Item 2(e)          CUSIP NUMBER: 61420L 10 4

Item 3             IF THIS STATEMENT IS FILED PURSUANT TO RULES 13D-1(b) OR
                   13D-2(b), CHECK WHETHER THE PERSON FILING IS A: Not Applicable

Item 4             OWNERSHIP

Item 4:(a)         AMOUNT BENEFICIALLY OWNED:                      COMMON STOCK
                                                                   ------------
                   Advent VII L.P.                                      0
                   Advent Atlantic and Pacific II L.P.                  0
                   Advent New York L.P.                                 0
                   Advent Industrial II L.P.                            0
                   TA Venture Investors Limited Partnership             0

Item 4(b)          PERCENT OF CLASS:                               PERCENTAGE 
                                                                   ----------
                   Advent VII L.P.                                      0%
                   Advent Atlantic and Pacific II L.P.                  0%
                   Advent New York L.P.                                 0%
                   Advent Industrial II L.P.                            0%
                   TA Venture Investors Limited Partnership             0%

Item 4(c)          NUMBER OF SHARES AS TO WHICH SUCH PERSON HAS:
                   (i) SOLE POWER TO VOTE OR DIRECT THE VOTE:     
                                                                   COMMON STOCK
                                                                   ------------
                   Advent VI L.P.                                       0    
                   Advent Atlantic and Pacific II L.P.                  0
                   Advent New York L.P.                                 0
                   Advent Industrial II L.P.                            0
                   TA Venture Investors Limited Partnership             0
                   (ii)  SHARED POWER TO VOTE OR DIRECT THE VOTE:       N/A
                   (iii) SOLE POWER TO DISPOSE OR DIRECT THE 
                         DISPOSITION:                             
                                                                   COMMON STOCK
                                                                   ------------ 
                   Advent VII L.P.                                       0       
                   Advent Atlantic and Pacific II L.P.                  0
                   Advent New York L.P.                                 0
                   Advent Industrial II L.P.                            0
                   TA Venture Investors Limited Partnership             0
                   (iv)  SHARED POWER TO DISPOSE OR DIRECT THE 
                         DISPOSITION                                    N/A

Item 5:            OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS: Not Applicable

Item 6:            OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER
                   PERSON: Not Applicable

</TABLE>


<PAGE>   4
 
SCHEDULE 13G                                                   Page 4 of 4 Pages
 

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<S>         <C>    <C>
Item 7:            IDENTIFICATION AND CLASSIFICATION OF THE SUBSIDIARY WHICH ACQUIRED
                   THE SECURITY BEING REPORTED ON BY THE PARENT HOLDING COMPANY:
                   Not Applicable

Item 8:            IDENTIFICATION AND CLASSIFICATION OF MEMBERS OF THE GROUP:
                   This schedule 13G is filed pursuant to Rule 13d-1(c). For the
                   agreement of group members to a joint filing, see below.

Item 9:            NOTICE OF DISSOLUTION OF GROUP: Not Applicable


Item 10:           CERTIFICATION: Not Applicable
</TABLE>


SIGNATURE
After reasonable inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this statement is true, complete and correct.

AGREEMENT FOR JOINT FILING
Advent VII L.P., Advent Atlantic and Pacific II L.P., Advent New York L.P.,
Advent Industrial II L.P. and TA Venture Investors Limited Partnership hereby
agree that TA Associates shall file with the Securities and Exchange Commission
a joint schedule 13G on behalf of the above-named parties concerning their
beneficial ownership of Network Appliance Inc.

Dated:


ADVENT VII L.P.
By: TA Associates VII L.P., its General Partner
By: TA Associates, Inc. its General Partner

By: /s/ Katherine S. Cromwell
    ----------------------------------------------------
    Katherine S. Cromwell, Managing Director

ADVENT ATLANTIC AND PACIFIC II L.P.
By: TA Associates AAP II Partners L.P., its General Partner
By: TA Associates, Inc. its General Partner

By: /s/ Katherine S. Cromwell
    ----------------------------------------------------
    Katherine S. Cromwell, Managing Director

ADVENT NEW YORK L.P.
By: TA Associates VI L.P., its General Partner
By: TA Associates, Inc. its General Partner

By: /s/ Katherine S. Cromwell
    ----------------------------------------------------
    Katherine S. Cromwell, Managing Director

ADVENT INDUSTRIAL II L.P.
By: TA Associates VI L.P., its General Partner
By: TA Associates, Inc. its General Partner

By: /s/ Katherine S. Cromwell
    ----------------------------------------------------
    Katherine S. Cromwell, Managing Director

TA VENTURE INVESTORS LIMITED PARTNERSHIP

By: /s/ Katherine S. Cromwell
    ----------------------------------------------------
    Katherine S. Cromwell, General Partner