Defeated Klopp upbeat despite Dante let-off
Dante was already on a yellow card when he kneed the impressive Marco Reus in the chest to concede an obvious penalty but Italian referee Nicola Rizzoli did not reach for his pocket.
Ilkay Gundogan converted the 68th-minute spot-kick to equalise Mario Mandzukic's opener on the hour but Arjen Robben grabbed Bayern's winner a minute from time.
"I saw it in the game and I was sure you can give a second yellow card and when I saw it on television I thought you had to give it," Klopp told a news conference when asked about Dante's escape.
However, in typical style the excitable 45-year-old tried to see the bright side.
"In the history of football there were refereeing decisions worse than this. Eleven against 10 after that we are the winner? I don't know."
Klopp lives and breathes every kick of a match and at one stage celebrated Neven Subotic's clearance off the line as wildly as when his youthful side netted the leveller in the first all-German final in Europe's premier club competition.
He is one of Europe's most talked about coaches, with reports even saying he turned down Bayern a few years ago before leading Dortmund to Bundesliga titles in 2011 and 2012.
The bearded German has also been linked with Arsenal among others but he is happy where he is, nurturing bright young players into some of Europe's best through an emphasis on skill not brawn.
Despite the disappointment of losing having dominated the first 20 minutes with a succession of trademark counter-attacks, Klopp was already thinking about next season with Dortmund.
"We will come back, maybe not to Wembley but we will try to come back to another final," he joked.
"The team played a great game, they gave everything they had. They really deserved to equalise.
"I feel pride comes up in me and sadness goes way. It was a great season from my team and a really great match, perhaps the best match against Bayern in the Champions League this season."
Bayern beat Dortmund to the Bundesliga title and are the big bugbear having also taken Germany midfielder Mario Gotze from Klopp's side for next season.
Top striker Robert Lewandowski's future is also uncertain and the coach, who has had to rebuild his side after previous high-profile departures such as Shinji Kagawa and Nuri Sahin, knows the end-of-season beach might have to wait.
"Now we have to go on holiday, buy some players because others clubs want our players," he smiled.
"Next week I have much work to build a new team and then I hope I am on holiday.
"I think we'll get a pretty decent team together, I wouldn't worry about that."