The Reds moved up to fourth place in the Premier League after goals from Roberto Firmino, Nathaniel Phillips and Alex Oxlade-Chamberlain at Turf Moor.
Firmino broke the deadlock in the 43rd minute of the contest, before Phillips' first goal for the club was followed by a clinical finish from substitute Oxlade-Chamberlain in the second half.
The result sees Klopp's side move ahead of Leicester City on goal difference with one fixture remaining in the campaign.
Read on for a transcript of the boss' post-match press conference...
On his feelings on Liverpool moving back into the top four with a game to go…
I couldn't be more pleased, to be honest. I never expected that. It's not that I take this for granted, I knew this season is for us an incredibly tough, tough season. I heard now that on Valentine's Day, February 14, was the last time we were in the top four because we didn't win a lot of games since then. But now in the last eight, 10, I don't know exactly how many games, we are back on track and if we win on Sunday then probably – it depends on the result of Leicester or Chelsea – then we are probably qualified for the Champions League. It's insane that we came that close, but we are not through. When you win the semi-final you go to the final. That's where we are and we will give our absolute everything to win that as well.
On how Liverpool managed to put themselves into this position heading into the final game…
Just keep going, keep believing, keep improving. Don't put two games in one, like thinking about this or that – stay focused on the next one, don't think about the game after that. These kind of things, it's not massive, you just have to keep going and that's what we did. It's incredibly tough for the boys in the moment and you need to be lucky in moments as well, that's clear. For tonight it was good enough and we need to make sure we will be good enough as well on Sunday.
On how pleased he is for Phillips...
Very pleased, very pleased. I love the boy, he knows that. If we really make it or not, whatever, let's talk after the Crystal Palace game. Just let's finish this season and then if you want I write a book about both boys – about Nat and about Rhys, it's no problem. But let's please play this game and let the boys stay focused, let them recover and all these kind of things. Then we can talk about that. I promise you if you want I answer [for] an hour your question.
On what he thought about tonight's performance...
Really good, really mature performance with not a world-class start, let me say it like this. In the beginning we looked quite a little nervy, our passing was really not accurate enough, we gave too many easy balls away and made it too easy for Burnley. But after around 15 minutes we found our feet back and then we played really good football, that's true. It was very helpful tonight to play that kind of football, score those kinds of goals. We missed the two big chances maybe of the game in the beginning, but the way we played there already was really, really good. [We] scored a wonderful goal. Second goal from Nat, outstanding skill from Sadio, nice little chip and great, great header. And the third goal, Oxlade at his best. It looks like timing is right but [it's] not done yet, we know that. Without that kind of performance, you have no chance here. Burnley is really too strong because the way they play, the way they went for our centre-halves obviously tonight, that's so tricky to defend and the boys did really well and we needed each single good performance on the pitch tonight.