Chelsea threw away a two-goal lead against the League One side at Stamford Bridge, ending any hopes of winning an unprecedented quadruple.
Mourinho branded the 4-2 defeat a ???disgrace??? and will now hope his side bounce back against Liverpool on Tuesday in the Capital One Cup semi-final second leg.
The tie is finely poised at 1-1, with a place in the March 1 final at Wembley at stake.
Mourinho expects a response from his established first-choice players after making nine changes for Bradford’s visit and seeing his fringe players disappoint.
“I always said I don’t choose competitions, that we go match after match,” Mourinho said, with his team still well poised in the league and also gearing up for a Champions League last 16 clash against Paris St Germain.
“The most important competition now is the Capital One Cup, because it’s the next game we have to play.
“Obviously the Premier League is in front of the cups, but the way we prepare things – in a serious way, in a professional way – I can’t say we don’t care about the FA Cup. ‘Ah, we lost, I don’t care’ – I cannot say that.
“We lost and we care. I cannot say more than that. Does this affect the next match? I don’t know.
“Because many of the players were not directly involved in the game, I don’t think these players can be affected. I don’t think (Branislav) Ivanovic, (Nemanja) Matic, Diego (Costa), can be affected by something that is not directly related to them.
“But it’s our team and we lost at home against a lower division team.”