Mane was left out of the starting lineup as Liverpool visited Old Trafford, with Roberto Firmino starting in his place and going on to score twice.
It was a vital win for Liverpool, which keeps them in control of their fate in the top-four race, but despite the significance of the result, Mane was clearly unhappy after the final whistle.
Klopp approached his No. 10 for a customary post-match handshake, but found himself dismissed, which has been seen as disrespect from Mane towards his manager.
But in his pre-West Brom press conference on Friday, Klopp has played down headlines on the situation, comparing it to his experience as a player.
“If somebody shows me five million times respect, and one time not, what is then more important?” he asked.
“The world is in a situation where you then make this one time bigger than necessary. That’s unfortunately the case.
“I hope for you that your boss would not forget, if you don’t show him respect one time, all the other stuff.
“Even when I speak now about that already, I can see the headlines you are making of it. That’s not the case, I’m completely relaxed about that.
“If you would have seen me as a player, all that I did out of emotion, that was insane! I’m a completely normal guy, and it happened to me anyway.
“Nothing else, we will talk about it and then it will be sorted. That’s all.”
Klopp revealed that he was yet to speak to Mane due to the short time between returning to Merseyside and his press conference, but stressed that “everything will be fine.”
“I can imagine you dreamt all night about it! I cannot make a bigger story of it than it is,” he joked with journalists.
“Football is an emotional game and everybody expects from us that we control out emotions always. That doesn’t work out always, that’s the case.
“It happened to me as a player, it happened to other players when I was their coach.
“We had, so far, no real chance to talk about it, but we will and there will be nothing left. Everything will be fine.
“Do we want these things to happen? No. But it’s not the first time in my life and I’m afraid to say it will probably not be the last time. So that’s it.”
Mane could return to the side for Sunday’s clash with West Brom, with Klopp not expecting any new fitness concerns to emerge from the win in Manchester.
He said: “It’s pretty early still after the game. We came home pretty late last night, so far I heard nothing about [injuries].”