The result is rubbing salt in the wounds of thousands of locked supporters from the Stade de France in a chaotic scene.
The kick-off at the European Club Football Showpiece was delayed by more than half an hour.
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Police fired tear gas canisters at fans, who tried to disperse the crowd around the stadium.
Liverpool said in a statement: “This is the biggest match in European football and fans don’t have to feel the scene we saw tonight.”
Earlier in the evening, Liverpool legend Kenny Dalglish laid a wreath in honor of the 39 people killed in the Hazel disaster before the 1985 European Cup final.
Despite security failures another tragedy was averted as UEFA was responsible for the fake tickets.
Less than a week ago, the Reds were on the brink of an unprecedented quadruple.
Instead they will have to settle for a league and FA Cup double after being deprived of big prizes in the Premier League and Champions League.
Manchester City claimed the English title by one point after the dramatic final when Pep Guardiola’s men lost 2-2 to Aston Villa 2-0.
Heartache for Liverpool at the end of an incredible season 💔 #UCLfinal https://t.co/RaHtfDqOPe
– UEFA Champions League (haChapterLeague) 1653778701000
“These guys played an outstanding season,” Klopp said. “The two competitions that we didn’t win, we didn’t win by the smallest possible distance.
“City were one point better and Madrid were one goal better tonight.”
Vinicius Jr. scored the only goal as he stole Fede Valverde’s cross-cum-shot to return the back post.
But the fact is that Madrid goalkeeper Thibaut Courtois, who has been named Man of the Match, says more about the flow of the game.
“Something is wrong with the other team when the goalkeeper is Man of the Match,” added Klopp. “They scored a goal and we didn’t. That’s the simplest explanation in the football world.”
Pain and ecstasy. #UCL Final https://t.co/sWpx7kHcSx
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For the third time this season, the club’s men failed to fire in the final.
They lost twice to Chelsea in a penalty shootout after 120 goals without a goal at Wembley.
But Madrid were not so forgiving because they had a tremendous run cap through the competition to claim the 14th European Cup.
Klopp has now won just one of his four European Cup finals.
Four years ago, Kiev Real won 3-1.
Liverpool return to Madrid a year after winning their sixth European crown.
And Klopp is confident his team will not stop at the showpiece for the third time in five years.
“The difference between now and 2018 is that I see them coming again,” he said. “I wanted it but I didn’t know it. They have an incredible attitude. It’s a great team and we’ll go again.”