Mane was left on the bench for the encounter with the reigning league champions, coming on only late in the game as the Reds sought to find a late winner.
His involvement was minimal, given the delay in bringing him on, and there were suggestions that he was unhappy with the manager at not playing a bigger role.
But Mane has rejected such talk, instead making it clear there was only a discussion over his positional work in the closing stages.
“He [Klopp] 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 also lauded fellow forward Salah, whose goal on the day was his 15th of the season already in a Liverpool shirt.
“He’s doing very well for us and we are happy to have him in the squad.
“He is a very important player for us and I’m going to keep trying to help him score more goals for the team.
“He is a very, very good player for us and [if you give him] space he is unbelievable. No-one can catch him and also he is clever.”
Mane has set up two of Salah’s goals thus far and the duo give Liverpool a frightening edge to the attack with their pace and direct running toward goal.
With such a heavy fixture list upcoming it was no surprise to see changes made against Chelsea, though Reds fans will hope to see the two in tandem from the start whenever possible.