Mane, who was named on the bench for the fixture, refused to respond to Klopp's approach after the final whistle at Old Trafford and was even caught on the television cameras walking towards the tunnel shaking his head.
The manager played down the relevance of the incident ahead of Liverpool's next game against West Brom.
"I cannot make a bigger story of it," Klopp told reporters at his press conference.
"Football is an emotional game and people expect that we control our emotions always but it doesn't work out that way. We will talk about it and everything will be fine."
Klopp was quick to highlight the glowing respect Mane has demonstrated for much of his Anfield career.
"If somebody shows me five million times respect and one time not, what is more important?" Klopp responded. "I hope for you that your boss, if you one time don't show him respect, doesn't forget the other stuff."
He went on to add: "I can already see the headlines, but it is not about that. I am completely relaxed.
"I am a completely normal guy. We will talk about it, and then everything will be fine."