Klopp added next year's final in Istanbul was already a target, advising supporters: "Book the hotel!"
A 1-0 loss to Madrid at Stade de France meant Liverpool was left with FA Cup and Carabao Cup triumphs to show for a season in which it threatened an unprecedented quadruple.
Manchester City denied it the Premier League title on the competition's dramatic final day last weekend, and it was UEFA Champions League specialist Madrid that toppled the Reds on Sunday (AEST) to claim a 14th European crown, with Vinicius Junior netting a second-half winner as Thibaut Courtois excelled in goal.
"Everyone in the dressing room, nobody feels it was a great season at the moment," Klopp said after the loss. "We probably need a few minutes for that, maybe hours."
He said two decisions had gone against Liverpool by "the smallest margin possible", but did not specify which incidents he was referring to.
"We played a good game, not the perfect game," Klopp added. "We had a lot of shots but not the clearest, only three or so where [Thibaut] Courtois made top saves.
"Then we conceded a goal... Vinicius was there and that was it."
Klopp said Liverpool tried "absolutely everything" after he had told his players to "be more brave in the second half".
Vinicius struck just before the hour mark, and Liverpool huffed and puffed but was not at its best as Madrid repelled the threat of Sadio Mane and Mohamed Salah, with Courtois outstanding as the last line of defence.
The Belgian made nine saves in the match, the most on record by a goalkeeper in a single UEFA Champions League final (since 2003-2004).
Klopp added he was alone among the Liverpool contingent in being able to put the game swiftly into perspective.
"It's not hard. I have that already, but I'm the only one in the dressing room," he said.
"I know it's not the success you want to have, but I have the strong feeling we will come again. That's how it is, because the boys are competitive.
"We have an outstanding group together and will have again an outstanding group next year. Then we go again. We obviously have to try a bit more often than others but no problem.
"Where's it next year? Istanbul? Yeah, book the hotel."