The Spanish giants looked on course to exit Europe's grandest club competition when Sergio Ramos' own-goal shortly after half-time gave United the initiative in the second leg at Old Trafford.
But the encounter was turned on its head when Nani was given what seemed a harsh red card in the 56th minute for a mid-air challenge on Alvaro Arbeloa.
Luka Modric levelled on the night and on aggregate with a spectacular strike from distance 10 minutes later before, inevitably, former United old boy Cristiano Ronaldo scored what proved to be the winner shortly afterwards.
While much of the attention was focused on Nani's sending off, Mourinho preferred to salute the efforts of his opponents.
"Independent of the decision, the best team lost. We didn't play well, we didn't deserve to win but football is like this," the Portuguese told ITV1 in a brief interview.
"I'm not speaking about the decision because I'm not sure about it."
When pressed further, Mourinho quickly added: "But independent of that the best team lost."
Madrid came into this match after back-to-back morale-boosting victories over fierce rivals Barcelona in the Copa del Rey and Primera Division respectively.
While Mourinho acknowledged United are a great side in their own right, he was left frustrated by his team's performance.
"They were very aggressive, they were very well organised tactically and the match was very difficult for us," he said on Sky Sports News.
"But I doubt that 11 against 11 we can win that match.
"I'm a bit frustrated because we played amazingly well against Barcelona and today [Tuesday] I was waiting for more.
"I wanted my team to come here and to express our football in a different way.
"I know they are giants, not just physically but also mentally, I know they are fantastic and I know they have a manager who can motivate and organise people.
"But I was wanting us to come here and play in a different way."
While they have taken huge steps towards potentially being crowned European champions this season, Mourinho is aware there are still plenty of challenges to overcome.
"We've beaten one but the Champions League is full of good teams," he said.
"But this one was an important one especially after the result of the first leg and with a bit of luck we did it."
Mourinho refused to celebrate such an important victory and headed straight for the tunnel after shaking hands with Sir Alex Ferguson before the final whistle - a move that could be interpreted as attempting to curry favour with the United faithful.
The former Chelsea boss has made no secret of his desire to return to the Premier League and has been touted as Ferguson's eventual successor.
When asked about his love for the English game, the 50-year-old added: "I love it, everybody knows I love it and everybody knows one day I will be back - that's for sure.
"I have to be be back because I enjoy so much all the time and today [Tuesday], independent of the result, was brilliant."