Dortmund's Kehl says club can be proud of Champions League final performance
Dortmund were unable to make the most of several good chances in the first half, before Dani Carvajal headed in from a corner after 74 minutes to give Real the lead and Vinicius Junior fired home the second to seal the win.
The German club, who finished fifth in the Bundesliga this season, were playing in their first Champions League final since 2013, which they lost to rivals Bayern Munich.
"I think we played a great game, especially in the first half, a nearly perfect one," Kehl said.
"It would have been perfect, if we would have scored. I think that's the negative point, that we didn’t use our chances. In the end, we saw how strong Real Madrid can play in a final, and how they can deliver from standard situations.
"They were able to turn the game. Very bitter, because we were so close and we would have deserved it. But we can still be proud of what we have accomplished."
Dortmund, who last season stumbled on the final day to hand the Bundesliga title to Bayern, have had to contend with several near misses in recent years, with their defeat to Real ensuring a third straight campaign without silverware.
Defender Nico Schlotterbeck said he felt sorry for Dortmund fans, adding: "It hurts that we played very well, but we are still going home with a 2-0 defeat. It is brutal, but in football not always the better team wins.
"The fans were incredible today. They were great in delivering here and in Dortmund. They already suffered last year and now this. But I can say, that we will get a title for the fans and will celebrate."