The debutant, with the score at 2-1 in City's favour, dived into a 50-50 challenge with United captain Wayne Rooney.
Mourinho is convinced it should've been a penalty and Bravo also should've seen red.
He told MUTV: "Bravo was a penalty and a red card.
"If any player does that outside the box, it's a direct free-kick and a red card. Inside the box it's a penalty and a red card.
"But the referee...
"Well, maybe he knew the consequences of making that decision. The consequences are it would be a very different game."