The Reds confirmed their place in the draw for the last eight of the competition with second-half goals from Mohamed Salah and Sadio Mane in Budapest, producing a 4-0 aggregate victory in the last-16 tie.
Extended highlights: LFC 2-0 RB Leipzig
Afterwards, Klopp spoke to reporters about the importance of the win, his side's hopes in the Champions League and the performance of European debutant Nathaniel Phillips.
Read on for a summary of the boss' post-match press conference...
On whether tonight was what Liverpool needed…
Yeah, but the performance led to that. The performance was very important, the level we played tonight was really good and was necessary as well because Leipzig is a tough opponent. We did really well, I have to say. Defending-wise, it was good. The last line, the two centre-halves did really well and with the three up front, of course it helps with Fab playing in the No.6, it gives Gini freedom in other areas and this kind of thing. Thiago did well, the front three worked well together, defensively first and foremost but offensively then it worked out as well. We missed a couple of chances in the first half, big ones, but we closed the game in the second half and I am very happy with tonight, of course.
On Fabinho being back in midfield…
It was my hope before the season [Fabinho playing in midfield] and during the season it didn't happen, so we have to see what solutions we can find for the next games – for Wolves first and foremost. Of course, No.6 is his position, one of the best in the world in that position, it's clear. It was not only defending-wise really good from him, he played some good stuff as well. [He is] important for us.
On whether Liverpool will 'target' the Champions League…
It is kind of, but as well not because the only reason you play in this competition is because you want to win it. I am not silly, we know so far this is not a season which it will look like we will win the Champions League in the end, but that doesn't mean we don't want to go as far as possible and then we will see what is possible for us. Now we have to wait for the draw; it will be extremely tough games whoever we get, but we don't really think that far, we don't have to. We think from tomorrow about Wolves and then I don't know when the draw is, to be honest. We have to wait a little bit, no problem, then we will know, we will prepare for that and then we will see how far we go.
On whether Liverpool could be very dangerous opponents because they may target the Champions League...
We are, of course we could be that. I don't want to sit here now and want to create headlines about our Champions League performance and stuff like this. In the Champions League, we had kind of momentum during the season and in the Premier League not yet. But we have still enough games to try to get that back and win football games in the Premier League as well – and that would be helpful for the Champions League as well definitely.
On the display of Phillips...
What a boy he is, what a player he is, what a night it is for him. That's absolutely great. The concentration level he shows now nearly week in, week out since he's playing for us is absolutely incredible. He's doing exactly the right things in the right moment. In the air he's a monster but you could see it today, he's football-wise not bad, really good. I couldn't be happier for somebody than I am for Nat in this moment because it was a great game and not a lot of people get the honour to play a Champions League game. He has that now, he played a really good one, he won it and he's qualified for the last eight in Europe – that's really special. A few years ago nobody would have thought that and I'm really glad that he can experience it now.
On whether it will be easy to build momentum from this game...
It will help, that's how it is. It will help but we know that Monday at Wolves is a different kind of game. But if we play as good as we played tonight then it will be tough for Wolves, that's clear. But then we have to score and we have to defend, we have to deny them and we have to break through on the other side and all these kind of things. Tonight we played a really good first half but we didn't score with really big chances. The game was a little bit like a summary of our season, so we are good, we create chances but we don't finish them off often enough. But tonight then we had the second half and used it there, that's all fine. It's much better than if we would have lost tonight and would have been out of the competition – that wouldn't have helped at all. But that can help and we can see on Monday how much.