Borussia Dortmund paid the ultimate price for failing to take their chances against an incredible Real Madrid side, the Bundesliga club's coach Edin Terzic (41) said after the Spanish team's 2-0 triumph in Saturday's Champions League final.

After Dortmund wasted several good opportunities in a one-sided first half, Dani Carvajal and Vinicius Junior struck late to secure Real's 15th European crown.

"We didn't show the efficiency to score," a visibly downcast Terzic told reporters. "This is something we have to learn from."

Dortmund, who finished fifth in the Bundesliga this season, reached their first Champions League final since 2013 when Wembley also hosted their defeat by Bayern Munich.

They gave their all on the night, as did their incredible supporters.

"I am proud, that is the first thought, a proud moment," Terzic said.

"We brought nearly 100,000 people to London and everybody had the belief we could make it. It was a fantastic journey this year in the Champions League - a great campaign - but to be honest it is a little empty inside. It was a great opportunity to win it and we unfortunately didn't make it."

Dortmund CEO Hans-Joachim Watzke could not hide his disappointment.

"We did it well, should have taken the lead in the first half but then we got a bit tired and they were ice cold how they scored," he said.

"We knew what we can do. We are happy to have been here but when you dominate the game and have these chances and then lose then it is very disappointing."

Dortmund centre back Mats Hummels agreed.

"We had four chances and we should have scored one of them. We had so many chances and you just have to score," he said.

"At the end of the day we should have defended a little better with their goals. But there is no one to blame for that. We played a good game."

Terzic tried to stay positive for the Dortmund fans.

"Thank you for your belief, don’t let the doubt take over," he said. "We’re going to bounce back, we’re going to learn from this."