Vini Jr struck the only goal of the game in Paris.
Benzema said: "We deserved the final we got today, it was a beautiful game. A tough clash, one of the most difficult in the Champions League because there is so much history with this team. In the end we showed everybody that we're here, alive and winning things.
“A final is always going to be hard, it's really tough work, so tiring. We're LaLiga champions and we came into the game on a good run of form. We scored the offside goal and that got us into the game. In the second half we played like we always do, to win in the final.
“It meant so much to win it with Madrid, the best club in the world and in France, my country. It's so important to me, alongside all the fans, the madridistas. I'm incredibly proud."
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