Naby Keita, who came in for Thiago Alcantara, was withdrawn after just 42 minutes with Liverpool as an entire team thoroughly second-best in the Spanish capital in the first half.
Vinicius and Marco Asensio were both on the scoresheet before Mohamed Salah reduced the arrears early into the second half with what was Liverpool’s only shot on target all night.
But 20-year-old Brazilian Vinicius scored his second of the evening with 25 minutes to play as the La Liga giants, who face Barcelona in the Clasico this weekend, earned a thoroughly-deserved advantage to take to England next week.
Liverpool must win 2-0 or score four times if Real Madrid net once at Anfield if they are to progress to the semi-finals, where they would take on either Chelsea or Porto.
And Klopp told BT Sport: “If you want to go to the semi-finals you have to earn the right to do so. We didn’t do that tonight, especially in the first half.
“I really thought that would’ve been possible but now we have to show it in the next game. We cannot show it anymore tonight. We made it too easy for them, that’s the main thing.
“The goals in the end, they were the quick-thinking of Real Madrid and we were a little bit late. These mistakes can happen.
“I wasn’t happy with the way we played football when we were in possession. We had to play better football. We didn’t deserve a lot more tonight. The goal we scored in the second half was OK and gives us a lifeline.
“Intensity with the ball especially [we need more of in the second leg]. You can’t defend the speed of Real Madrid when you give them the ball in the wrong moments.
“If you lose the ball and you lose it in the right moments, you are in formation, you play counter-press, can win the ball back.
“That is not good. We have to be in possession much better and defensively as well. It’s not about the last line, it’s about what we do in front of that.”
“It was tactical. I could have done a few more changes in that moment. Thank God I didn’t! It’s just that.”
Liverpool’s captain on the night Gini Wijnaldum reflected to BT Sport: “It was difficult. I think because we played against a good side and the way we did it in the first half was not good.
“When we recovered the ball we lost it too quick with simple passes. I think that was the reason why we couldn’t come into our game.
“What we did at the weekend quite well, we recovered the ball when we counter pressed and when we had the ball we played good football.
“We didn’t do that in the first half, we lost the ball too easily and I think two moments where we were not concentrating enough, they scored.
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“We just said [at half time that] in the second half we have to play our football, don’t lose the ball too easily and concentrate more than in the first half.
“We had to stand better at the back, because they were a few times dangerous with the long balls, and also in the second half, I have to say.
“Just play our own game. I think that’s why we scored our goal, but unfortunately they scored again but it makes it more difficult than when it’s 2-1.
“It gives us confidence, of course. Of course we hoped for a better result now but we have to hang on the good things and that’s the away goal.
“Now we just have to make sure we score two to win and don’t concede an away goal.”
Liverpool take on Aston Villa at Anfield in the league on Saturday (3pm) before their return leg against Real Madrid next Wednesday (8pm).