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 second-round tie, which ended 1-1 at Valley Parade.
The League Two club have until 5pm on Friday to appeal the decision, but if they are unsuccessful, Uwe Rosler's side will be given a bye to face either Southend or Bury in round three.
Devlin 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.
"The first we heard of anything was on Monday afternoon and internally we just held off before putting tickets out for sale for the replay and just waited for the FA's decision from yesterday's committee hearing.
"It is the FA's competition, the FA make the rules which we all know about. Whether we feel sympathetic or not does not come into play really. It is the FA's decision. I do have some sympathies with Bradford.
"It is entirely a matter for the FA and Bradford City Football Club. I don't think we will be asked to get involved any further at this stage."