Dortmund produced a largely impressive performance at Wembley but were made to pay for a host of missed chances as they came up short against the undisputed kings of Europe.
The German side came close through Niclas Fullkrug and Karim Adeyemi but second-half goals from Dani Carvajal and Vinicius Junior gave Real Madrid a staggering 15th Champions League trophy.
Mourinho was quick to console Terzic after Dortmund’s heartbreaking defeat and told him he should be ‘proud’ despite suffering a loss that will haunt him for ‘the rest of his life’.
Asked what he said to Terzic, Mourinho told TNT Sports: ‘He was saying that it’s very, very hard and I told him time is not going to help you, it’s going to be very hard for the rest of your career and for the rest of your life.
‘But you must be very proud of the work you did because you did amazing. As a coach you could not do any more. The coach cannot score or put the ball in the net.
‘He can organise and give mentality and confidence and he did all of that. The approach was amazing. They were brave.
‘They did everything well except from scoring, as a coach he must be proud but he’s not going to forget tonight.’
Despite underwhelming in the Bundesliga – finishing fifth, 27 points behind surprise champions Bayer Leverkusen – Borussia Dortmund flourished in Europe, beating Atletico Madrid and Paris Saint-Germain on their way to the final.
But they came up short against prolific champions Real Madrid and Terzic bemoaned his team’s wastefulness in front of goal.
‘We put in a great display and I think we deserved more than losing 2-0,’ he said. ‘From the first second we showed the whole world that we weren’t just here simply to play a final – but to win it.
‘We did so many things right, but they were ice-cold at the right moment, which is what we lacked today. We played a fantastic game and were close to taking the lead.
‘But then the game turned around and Madrid showed why they are champions of this competition. We had good chances in the first half, like Madrid in the second, but we didn’t take them.
‘After the game, you can always ask the question what you should have done differently. I think we did many things right, but then a set piece changed the game.
‘We have to learn from that. We were playing well, we were dangerous on counterattacks. But we didn’t score. That was the difference today.’
While Dortmund left Wembley disappointed – as they did after losing the 2013 final to Bayern Munich – Real Madrid were crowned European champions yet again following their La Liga title win.
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