The Reds were a Sergio Ramos own goal to the good and in the ascendency when Nani was shown a straight red card by referee Cuneyt Cakir for a foot-high tackle on Alvaro Arbeloa just before the hour mark.
The decision completely changed the game and, courtesy of goals from substitute Luka Modric and Cristiano Ronaldo, Real came from behind to win the last 16 tie 2-1 on the night and 3-2 on aggregate.
Mourinho said: "Independent of the [referee’s] decision, the best team lost. We didn't play well. We didn't deserve to win. But football is like this. I am not speaking about the decision because I am not sure of it."
Real have recently produced two stunning wins over Barcelona but their failure to sparkle at Old Trafford was down to United’s superior tactics, according to Mourinho.
"My feeling is that Manchester United were playing very well, were very compact and aggressive in a good way," the Portuguese said.
"They were very tactically well organised and the match was very difficult for us. I had the feeling Modric changed the game as he brought qualities we did not have before.
"I doubt that 11 v 11 we win the match. I am frustrated as we played so well against Barcelona and today, I was waiting for more.
"I know United are giants, not just physically but mentally. I know they have a manager who can motivate them, but I was waiting for us to play