Jose Mourinho's side beat Bayern Munich 2-1 in regulation time in the return of their semi-final tie after losing the first leg with an identical score, but the Bundesliga giants eventually prevailed 3-1 on penalties, much to the disappointment of Sergio Ramos.
"We would have liked to reach the final, but this will not tarnish the great season the team have had and that we want to seal with the league title. Bayern were a great side. I'm proud of the team and of the season we're having," the defender stated to the official Madrid website.
"We tried everything but we knew we faced the likes of [Arjen] Robben, [Franck] Ribery and [Mario] Gomez. The match went through many different phases after our second goal. We can't attack all the time.
"We must move on. This hurts because the final was within our reach. It's a real shame to be eliminated in a penalty shoot-out. It is something you never want. We must hold our heads high."
The 26-year-old was one of three Madrid players to miss from 12 yards, but he stressed that he would take a penalty again if asked to do so.
"Penalty shoot-outs are unpredictable. I wasn't lucky to score my penalty, but I was confident and I would try it again tomorrow for the team. You feel great pressure, but I've always withstood it well."
Madrid resume La Liga action on Sunday when they host Sevilla. They hold a seven point lead over second-place Barcelona with four rounds to go.
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