Mane came on in the closing stages of the draw at Anfield on Saturday before having a discussion with Klopp after the final whistle.
However, the Senegal international played down the incident, saying it was a "friendly" conversation.
"He asked me to play on the right side and one time I tried to ask for the ball in the number nine position," Mane told Sky Sports News.
"Mo [Salah] was on my side and the coach was shouting, 'Sadio come onto the right side'.
"After the game I told the coach it was easier if you told Mo to come in because he was close to you.
"But it was friendly, it was not because I was unhappy or something else. There was no problem, I was just communicating and explaining that to him after the game."
Mane was surprisingly dropped from the starting line-up for the crucial Premier League clash as his team were left in sixth in the table.
The 25-year-old, who has three goals and two assists in the league this season, said it was tough to accept being on the bench.
"It was not easy for me. It was a difficult moment, but it’s part of football and it can happen," Mane said.
"It's important for me to come back now. I'm feeling very well."