Liverpool will 'come again' after Champions League defeat, says Klopp
The result rubbed salt into the wounds of thousands of supporters who were locked out of the Stade de France amid chaotic scenes.
Kickoff to European club football's showpiece was delayed by over half an hour.
Fans described being targeted by tear gas from police, who tried to disperse the crowds on the perimeter of the stadium.
"This is the greatest match in European football and supporters should not have to experience the scenes we have witnessed tonight," Liverpool said in a statement.
Early in the evening, Liverpool legend Kenny Dalglish had laid a wreath in honour of the 39 people killed at the Heysel disaster ahead of the European Cup final in 1985.
The fact another tragedy was avoided despite the security failings that UEFA blamed on fake tickets was the only consolation of the evening for Liverpool as on the field, their season ended in an anti-climax.
Less than a week ago, the Reds were on the brink of an unprecedented quadruple.
Instead they have to settle for the double of League and FA Cup after missing out on the bigger prizes of the Premier League and Champions League.
Manchester City claimed the English title by one point after a dramatic final day when Pep Guardiola's men came from 2-0 down to beat Aston Villa 3-2.
"These boys played an outstanding season," said Klopp. "The two competitions we couldn't win we didn't win for the smallest possible margin.
"City was one point better and tonight Madrid was one goal better."
Vinicius Junior scored the only goal as he stole in at the back post to turn home Fede Valverde's cross-come-shot.
But the fact it was Madrid goalkeeper Thibaut Courtois who was named man-of-the-match said more about the flow of the game.
"When the goalkeeper is man-of-the-match then something is going wrong for the other team," added Klopp.
"They scored a goal and we didn't. That's the easiest explanation in the world of football."
For the third time this season, Klopp's men failed to fire in a final.
"I don't want to talk about the contract. I'm staying next season for sure, let's see after that," said @MoSalah at Liverpool's pre-Champions League final media day on Wednesday 👇https://t.co/GE7D0iWxui— The New Arab (@The_NewArab) May 25, 2022
Twice they beat Chelsea in penalty shootouts after 120 goalless minutes at Wembley.
But Madrid were not so forgiving as they capped a remarkable run through the competition to claim a 14th European Cup.
Klopp has now won just one of his four European Cup finals.
Four years ago, Real also won a clash between the sides 3-1 in Kyiv.
Liverpool bounced back a year later to win their sixth European crown in Madrid.
And Klopp is confident his side will not stop at reaching the showpiece for a third time in five years.
"The difference between now and 2018 is I see us coming again," he said. "I wished it but I couldn't know it.
"They have an incredible attitude, it's a fantastic group and we will go again."