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 tie had been due to go to a replay but the FA announced they had expelled City from the competition 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.