The Red Devils saw their title defence come to a screeching halt this week as the Robins snatched a 2-1 win deep into second-half injury time at Ashton Gate to progress to the semi-finals.
And, speaking after the game, Mourinho moved to congratulate the Championship outfit on their success, but still felt they were fortunate to have stolen the win.
He told Sky Sports: "They were a bit lucky. But they fought a lot to be lucky. They won the game in our best moment, where we can't react, when everyone was waiting for our goal.
"So I have to say they were a bit lucky. Also in the first half, we hit the post twice.
"But they played brilliantly, fought like this was the game of their lives, which it probably was, and I think a beautiful day for football because a team from a lower division one. To get into a semi-final, a big day for them, their supporters.
"I congratulate them. I don't want me saying they are lucky to be the main thing of it. The main thing of it is that they won and fought hard for that.”