A 2-0 second-leg victory on the night was not enough for the Spanish giants to fight back against Borussia Dortmund as the German club progressed to the final 4-3 on aggregate.
It is the third season in a row Mourinho and Real have lost in the semi-finals but they had themselves to blame in the opening 25 minutes of their second leg this season.
As they sought to overcome their 4-1 first leg defeat by Dortmund in the battle to reach Wembley, Cristiano Ronaldo, Mesut Ozil and Gonzalo Higuain were among the players to miss good opportunities.
And Mourinho said: "My players have given everything. If we had scored earlier, we would have had a chance.
"The Bernabeu has been fantastic, the fans believed until the end but we did not make it."
Mourinho was unhappy with the decision of English referee Howard Webb not to send off defender Mats Hummels for a handball on the edge of the area.
He said: "I am very sad with one of my favourite referees in the world, I am very
"It is a red card for Mats Hummels, he saw it, everybody saw it but in that moment he was not a ref he was a human being. He thought 'if I give him a red card here, he misses the final'."
Goals in the last eight minutes of normal time from substitute Karim Benzema and captain Sergio Ramos eventually gave Real hope of a grandstand finish but it was not to be.
Centre-back Ramos said: "It is a shame. Sometimes you lose, that is football. In Dortmund, we should have played the way we did tonight.
"We feel for the fans. It is a shame to have been so close but the missed chances in the first half were costly."