Real very nearly staged a remarkable late comeback to progress to the final after goals from Karim Benzema and Sergio Ramos gave them a 2-0 win over Borussia Dortmund on the night, but the Germans' 4-1 victory in last week's first-leg saw them squeeze through 4-3 on aggregate.
And afterwards Mourinho refused to confirm that he will still be in charge of the Spanish champions next season.
"My future is not important, it is Real Madrid that are important," he said.
"I know that in England I am loved. I am loved by the fans and the media who are fair with me. They criticize me and give me credit when I deserve it.
"I know I am loved by the clubs, especially one. In Spain it is different because people hate me, many of whom are in this room, and it is difficult because I love the club and the president and we have made this team which is ready to achieve big things."
After a frantic opening 15 minutes by Madrid, in which they had three clear chances to score, Dortmund seemed to have drawn the sting from their opponents until the hosts' late onslaught, and Mourinho lamented not having scored during their early period of dominance.
"We started very strongly, with intensity, we pressured them and the circulation of the ball was excellent.
"The earlier you score a goal the better chance you have to come back. We missed important chances and that meant in the second half we had to risk everything.
"We were playing against a quicker team and had to adopt our way of playing which left a lot of space in behind. They had two great chances when (Robert) Lewandowski hit the bar and Diego (Lopez) made a great save but once we scored the people believed a little more.
"I'm proud of the way we kept going till the end."
However, Mourinho was less happy with the performance of English referee Howard Webb, who the Portuguese believes made a mistake in not sending off Mats Hummels for a deliberate handball in the second half.
"He was a man not a referee in this minute and he has to be a referee. He has to send off Hummels, it is not a penalty because it is outside the box but it is a sending off because Karim (Benzema) is clear through on goal."