The Reds claimed victory in the 239th Merseyside derby thanks to Mohamed Salah's double and finishes from Jordan Henderson and Diogo Jota.
Henderson broke the deadlock in the ninth minute with a well-taken strike from the edge of the box, before Salah doubled the Reds' advantage.
Demarai Gray pulled one back for the Blues but second-half efforts from Salah and Jota secured the win for Klopp's side.
Read a summary of the boss' post-match press conference...
On Liverpool’s performance…
It was, for sure, the best performance we’ve shown since I'm at Liverpool at Goodison. We had some good games here, but we were never as good as tonight. We were never as calm as tonight, we were never as convinced as tonight and that’s why we won the game and I am really happy about that.
On Mohamed Salah’s outstanding display…
Not only him, but of course him as well. Scoring these two goals, the first one was a pass from Hendo and the next one, he put Coleman under pressure. We saw a similar situation in the Chelsea – [Manchester] United game; even Jorginho, one of the best in the world, under pressure and a high ball is really tricky. He went and put that away, absolutely great. Diogo’s goal, outstanding. The performance of all of the boys was absolutely outstanding. I thought Sadio was in moments unplayable as well, so it was just a good performance.
On the display of Henderson...
Hendo was good but with his skillset you should be good. When you can train, when you can play, when you get rhythm and then you have the quality of Hendo, then you will play good football games. Tonight, I think it was for him as well the best performance at Goodison. Obviously since I'm at Liverpool we had to learn these kind of games. We had to learn to play at Old Trafford, we had to learn to play at Goodison, and tonight we showed that we made a big step in our development and that's really good. It doesn't mean anything for the future but it shows us that this is now our benchmark, that's what we have to reach now in each game when we play these kind of teams, because emotions are important in football. We are a very emotional football team but, first and foremost, you need the right mood and mindset. Yes, emotion [is] good but not the only important thing.
On why thinks it's 'step forward' for his side...
The two derbies for us against Everton and United are big games and you have to learn to keep yourself calm and together, if you want, to play your best football. To be 100 per cent, when I look back there was not one derby at Goodison where I thought, 'Wow, that was a great game, nearly perfect', so there is a lot of space for improvement. I wanted us today to be really mature and, yes, very aggressive but in a football way, angry as well but in a football way. So in the situation when you can get balls back, when you have counter-pressing situations, you cannot do that without a bit of anger and a bit of greed and all these kind of things, so you need that. But then there are moments when you just have to move and pass the ball around their formation or through their formation, and for that you need a different mindset – and that's what we had tonight.