The Reds eased to a straightforward win after Chris Wood’s own goal broke the deadlock before Mane and Roberto Firmino sealed three points.
The Senegal international was denied the opportunity to score his second goal moments before second-half substitution when Mohamed Salah selfishly opted to shoot on goal rather than play in his team-mate.
Mane was agitated and animated when he was replaced in the 85th minute and the African forward seemed to be unhappy with Salah’s decision not to square the ball to him with the goal at his mercy.
Both James Milner and Roberto Firmino managed to subdue the striker but Mane’s reaction was a talking point after Liverpool FC’s 13th successive victory.
Speaking to BBC Sport after Liverpool FC’s 3-0 win over Burnley about Mane’s reaction, Klopp said:
“But it’s good eh? He was upset, it was obvious.
“Sadio cannot hide his emotions, I like that. But all sorted. We spoke about it and everything is fine.
“We are individuals, we are emotional. It was a situation in a game. What else could have happened? It was not a phone call.”
Liverpool FC strikers Mane and Salah shared the Premier League’s Golden Boot with Pierre-Emerick Aubameyang last term after all three players finished the 2018-19 season with 22 goals.
The Reds will welcome Newcastle United to Anfield in their next Premier League game on Saturday 14 September.
Liverpool FC haven’t won the Premier League title but have finished in second place in 2002, 2009, 2014 and 2018.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news