Mane was not in the Liverpool starting XI for their match against the Red Devils, and was only brought on as a substitute in 74th minute.
Mane, who was upset he had not been included in the starting XI, snubbed Klopp's offer of a handshake after the game, which was caught on camera.
Speaking ahead of Liverpool's Premier League clash with West Bromwich Albion, Klopp revealed he and Mane have spoken about it, and that the player has apologised to him for his act. "We spoke and he apologised. That's clear and that is it," Klopp told Sky Sports [via Goal].
Meanwhile, Klopp had played down Mane's reaction and insisted there is no problem between himself and the Liverpool attacker after their win over Man United itself. "No, no problem. I made a late decision in training to decide for Diogo [Jota]. The boys are used to me explaining things usually but there was actually no time for that and that's all. It's all fine," the Reds manager had told Sky Sports.