UEFA has announced that referees' decisions are viewed as final unless it is a case of mistake identity, though it will review Ibrahimovic's dismissal next week to decide whether it merits a greater sanction.
PSG coach Laurent Blanc said the club would consider making an appeal, but UEFA's position means Ibrahimovic will be suspended for at least one match as a result of his red card, which was shown for a foul on Chelsea midfielder Oscar.
A UEFA spokesman pointed to its disciplinary regulations which state: "Decisions taken by the referee on the field of play are final and may not be reviewed by the UEFA disciplinary bodies."
Mourinho said after the 2-2 draw which saw PSG win on away goals that he "hopes UEFA can minimise the mistake."
He said: "He would tell me if there was a reason for a red card. He was very disappointed. If that's the case I hope they can minimise the mistake and let him play in the quarterfinals because if he did nothing wrong he deserves that."
Blanc said after the game: "There will be a committee who will convene to talk about the decision and I hope he will be in our party for the quarterfinal."
Manchester United failed in an attempt to overturn a red card for Darren Fletcher in 2009 after he was sent off in the Champions League semifinal against Arsenal despite video replays showing he had made little if any contact, and the Scotland midfielder went on to miss the final.