Late goals from Karim Benzema and Ramos himself gave Los Blancos a 2-0 win on the night, but Jose Mourinho's side lost 4-3 on aggregate after a flurry of attacks in the closing moments.
“You can lose, but when you lose like this.....We have given everything here,” he briefly told reporters after the game.
Dortmund will face either fellow Bundesliga side Bayern Munich or Barcelona in the final at Wembley. Barca trail 4-0 but the second leg on Wednesday is at their Camp Nou home.
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