After a goalless first half at Turf Moor, Mane broke the deadlock for the visitors by finding the net in the 61st minute.
Burnley equalised through Johann Gudmundsson but Liverpool FC defender Ragnar Klavan netted deep into stoppage time to claim the three points for Klopp’s men.
Liverpool FC have been in good form in recent weeks, with Klopp’s side having won four of their last five Premier League games.
Mane has been one of the Reds’ top players of late and he has now scored eight goals and made five assists in all competitions for the Merseyside outfit.
Biographies: Find out more about Liverpool forward Sadio Mane
And Klopp picked out the 25-year-old attacker for special praise after the victory over Burnley at Turf Moor.
Speaking at his post-match news conference, Klopp said: “It’s obvious – Sadio is unbelievably important for us.
“In so many moments he is strong and quick. In the other moments it doesn’t click and then he scores a goal like this and you think, ‘wow!’.
“When he came into the dressing room the whole team got up and gave him [a round of applause] because they know.
“He will be back on top. He makes steps, that’s why I took him off. It’s a situation where sometimes you get an injury, and we need him so much for all the things coming.
“That’s it. I am happy. I had a lot of players in moments where it was not clicking, if you want, but they never scored. Sadio still scores, so that’s really cool.”
Liverpool FC now switch their attentions towards FA Cup affairs and their third-round clash against derby rivals Everton at Anfield on Friday night.
The Reds are fourth in the Premier League table as they look to try and secure Champions League qualification for the second season running.
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