Despite conceding a late equaliser, Klopp believes that the clash was a "fun" match to be involved in.
"If you ignore the fact that we played in Madrid today, then it's possible to call this a normal football match, in which both teams played at a very high pace and challenged their opponent in all aspects," said Klopp.
"My team were superb in the first half and in the second we showed a lot of passion. We were under plenty of pressure towards the end of the game, but I'm certain that we could have scored a third goal if we had broken through cleanly.
I think that Jose Callejon was brought on to win free kicks and one of those led to the equaliser. Of course it's a shame to concede that goal in the later stages of the game, however, overall it was a lot of fun and a very intensive match. We forced our opponents to all kinds of things that they weren't necessarily willing to do. It was a great game."
Dortmund top Group D ahead of second-placed Real Madrid.