Jamie Vardy opened the scoring after only three minutes and the Foxes held on until the 52nd minute, when Mohamed Salah netted his 16th league goal of the season. Number 17 followed 24 minutes later and proved to be the winner.
Reds boss Klopp says fans will have enjoyed their victory.
He said: "You don't want to be 1-0 down but if you are 1-0 down that early in the game you want to see the reaction I saw tonight – it was the best reaction we showed so far after being 1-0 down. It was fantastic.
"I didn't see one nervous player or any real reaction in a negative way. We kept on going and created and created and created, and played brilliant football. Defensively we were really strong. The main strength of Leicester is counter-attacking and quick transitions. If you are 1-0 down it plays into their hands and makes it more difficult. But we did really well. I liked the first half a lot apart from the result, to be honest.
"Everybody in the stadium reacted in the right way, everybody saw, 'wow, what a game!' It was 100 per cent one of the best we have played so far. We knew at half-time we had to carry on; there were not a lot of judgments that we had to change this or that.
"We had to do it again and again and again, and keep our nerves – that's the most important thing. Of course you get a little bit annoyed after missing the third or fourth chance. But they will come again. As long as we don't concede, we always have the chance to score. That's what we did – fantastic goals, two fantastic goals. They felt so good and felt so fair in this moment and deserved. So I'm really happy about it."