Arjen Robben's winning goal after 89 minutes crowned Bayern as European champions for the fifth time with a hard-fought 2-1 win at Wembley.
Mario Mandzukic's opening goal had been cancelled out by Ilkay Gundogan's equaliser from the penalty spot following Dante's foul on Marco Reus.
Dortmund's second Champions League final ended in defeat, but a rueful Klopp was convinced that his side could triumph in the competition first won by the club in 1997 in the future.
"I've told the players that we will come back - maybe not to Wembley but we will try to come back to another final. That's what I told them," said Klopp
"Congratulations to Bayern and Jupp (Heynkes) - you can't begrudge him the win.
"We were right in it but at the end, everything came together for Bayern and they won the game."