United led Madrid 1-0 early in the second half before the Portuguese winger was sent from the Old Trafford pitch for catching Alvaro Arbeloa on the arm with his foot when trying to control an aerial ball.
The decision was seen by many as the wrong one and it changed the whole complexity of the match as Madrid made the most of the one-man advantage to score twice through Luka Modric and Cristiano Ronald which gave them a 2-1 win on the night and 3-2 on aggregate in the Round of 16.
Mourinho told Sky Sports that he felt United were harshly done by: "Manchester United were playing very well. They were very compact, they were very aggressive, very well organised technically and the match was very difficult for us.
"I doubt with 11 against 11 we could win the match.
"I had a feeling that Modric would change the match because he brought to the game some qualities that we did not have on the pitch at the time.
"I am a bit frustrated because we played so well against Barcelona and today I was waiting for more. I know they (Manchester United) are giants, not just physically but mentally. I know they are fantastic and have a manager capable of organising and motivating people.
"But I was waiting for us to come here and play in a different way."