The Bantams did not receive written permission for Curtis Good, on loan from Newcastle, to play in the competition by the 12pm deadline on the day of the fixture, which ended 1-1 at Valley Parade. The FA announced they had expelled City from the competition earlier on Friday and gave them until 5pm to launch an appeal.
Bradford confirmed in a statement: "Bradford City Football Club can confirm that they will be appealing the FA's decision to expel the club from this season's FA Cup competition. This process will take place throughout the forthcoming week. The club will report any further information to its supporters when applicable."
Should the appeal prove unsuccessful, Brentford will progress to the third round to play Bury or Southend. Bradford admitted the error was "of an administrative technical nature" and have apologised to their fans.
An earlier statement read: "The nature of the charge is the playing of one of our loan players deemed ineligible due to the late submission for permission for him to play. Bradford City Football Club is very sorry to have to report such a matter and apologises to our fans.
"The error was of an administrative technical nature and not one to intentionally break competition rules.
"We presented a case of mitigation to the FA on Thursday, December 6, however the FA panel chose to enforce the full powers of its jurisdiction and have removed the club from the FA Cup competition."
Brentford chief executive Mark Devlin admitted he had sympathy with Bradford and would have preferred to have advanced in the competition on the pitch.
He told Sky Sports News: "It is not a satisfactory way to progress, we would much rather prefer to progress by winning a match but the FA have made their decision and that's it really."
Pending their appeal, Bradford are the only side left in three domestic cup competitions and face Barclays Premier League giants Arsenal in the quarter-finals of the Capital One Cup on Tuesday.