The Reds came to the Santiago Bernabeu on Wednesday night needing to overturn a 5-2 deficit from the first leg at Anfield three weeks ago.
And though the visitors created some good openings, Karim Benzema's late goal ultimately settled the outcome of the game on the night and ended any hopes of a comeback.
Read on for a summary of Klopp's post-match press conference in Spain…
On the result and performance...
We came here with the backpack we had with the three goals difference. You need a special performance and we didn't show a special performance tonight. It was, in moments, a good performance, but Real Madrid was, for the whole game, the team in control of the game. They had the better chances, Ali had to make two sensational saves to keep us in the game and that's the reason. Again, if you want to go through you need to be outstanding; if you want to win the game, you need to be really good. In the end, Madrid were the better team and that's why the right team went through to the next round.
On Real Madrid playing You'll Never Walk Alone following the full-time whistle inside the stadium as a mark of respect...
People told me, my staff told me after the game. It is a really nice gesture. We are two heavyweights who meet each other quite frequently in international football. I think it is clear we respect each other a lot and whoever did it, whoever was doing something like that, [made] a really nice gesture, I have to say. Absolutely. I was not angry after the game, but I was disappointed. I would be angry if we would have played better and it was close and then they win because of a penalty which was not a penalty or stuff like this. But in the end that all didn't happen. Real Madrid were just the better side and I am long enough in the business to respect that.
On whether fixtures like tonight's show the importance of being in the Champions League again next season...
Absolutely. With the history we have in this competition, we start usually in the competition with the idea of winning it, to be honest. We reached the final a few times, didn't win the final that often, that's true, but we were there three times in the last few years and that's why I believe if you want to win the competition, you have to be outstanding. We weren't tonight, so that's why it's then fair that we go out. But of course, it is the competition and we want to be part of it every year. That's a massive task for us, we all know that. When we come back from the international break we have a proper football week ahead of us, I would say, with three games: City, Chelsea and Arsenal, which will then probably define what we get out of it. People might say we lost it in Bournemouth, but I think this week is a pretty decisive one, so we have to hope now the boys come back healthy, early enough, in the right shape and then we will try it.
On the issues with VAR and the handball review at the end of the match...
I am now not in the perfect mood to discuss general football issues but these two games now, last night, if the whole world agrees it's not a penalty, and two guys think it is a penalty, then something is wrong. Tonight, I think that the VAR took the ref to the screen and asked him to watch it again, I don't know exactly what he is doing there because it's a clear deflection, it cannot deflect it from a closer range... so it's a clear deflection for the VAR, so keep on going. Everybody, again, with a football brain thought it was not a penalty. I arrived there and talking to Carlo and he said, 'It's not a penalty, it's deflected.' I know but he was still sent to the screen, so there is something not 100 per cent right. In the end, it was not a penalty, it was not decisive, they gave the penalty last night [and] it was a bit more decisive... in the end it is not our problem tonight but in general I think it would be cool if VAR is there to make the right decisions not the wrong [ones].
On the importance of reaching the top four now to qualify for the Champions League...
Our job is to squeeze absolutely everything out of this season what is possible. It's a strange one. Our recent two games, obviously a sensational performance against Manchester United, which is a real good football team. And then a really bad performance against Bournemouth, which is a good football team as well, but we should not lose this kind of game. It put us then under more pressure. If we could have three points then I think everybody really could have felt, or smell our breath, if you want. There is again distance because other teams won their games... it is clear, we want to be top four, but if we can do that, we will decide on the pitch [and] not here in the press conference.
On his second-half substitutions...
For Diogo, it was clear that he should not play now extremely long because he is still coming back from a long, long injury. You could see the game got harder and harder for him, little fouls there, one, two, three, he is not a player who is usually fouling so perhaps he comes a bit late. So, no risk with him and we have options on the bench. Yes, Darwin looked like he was not on the absolute top level as well and then we need to defend that side as well because conceding a goal is not helpful in that situation. Yeah, we can change there, that's why we did it. We wanted to mix it a little bit, that's true.