Liverpool avoided a first Premier League defeat of the season on Saturday as they came from behind to beat newly promoted Aston Villa 2-1 at Villa Park.
A VAR check for offside saw the goal stand, and there was more VAR misery for Klopp and his players minutes later.
Roberto Firmino found the net for Liverpool but was denied the equaliser as VAR reinforced the linesman's decision to raise his flag.
Liverpool, whose Trent Alexander-Arnold was making his 100th appearance for the club, had their chances to equalise throughout the second half but were wasteful as Mohamed Salah, Firmino and Adam Lallana all missed from promising positions.
Mane produced again in added time to give his team all three points, stooping to head in Alexander-Arnold's corner.
The Reds stayed top of the table on 31 points with the result, while second-place Manchester City similarly came from behind to beat Southampton 2-1 with a late winner.
Mane, booed every time he touched the ball after appearing to dive in the Villa penalty area, was Liverpool's driving force, missing a header in the first half then seeing Heaton save a couple of chances in the second prior to his winner.
"It was a perfect delivery from the corner, and in the end, I was even a bit lucky the ball went in," Mane said. "Today was not our best performance, but we deserved the three points. Aston Villa have been the team that pushed us harder so far. That's why this is the best league in the world, every single game can be like this one."