The Senegalese forward was only named on the bench for a crunch clash with the defending Premier League champions.
He was introduced late on and was clearly frustrated at the final whistle as he rowed with his manager on the field.
Klopp insists that Mane was not expressing his disappointment at being named among the substitutes, with their argument concerned with more tactical matters.
The German coach told reporters on the back of a 1-1 draw at Anfield: "I was shouting at him because he was in the centre.
“But no player's happy about that when you come on to the pitch with three minutes left and you feel like you've got 150 minutes in your legs already.
“He was not happy and said to me 'Mo [Salah] wanted to come in the position' but Mo already had 90 minutes in his legs.
"So it would have made more sense that Sadio was close to the right wing and starts from that position.
"It's not a big thing, we could have done it in the dressing room, it would have been the same thing. Everything is sorted immediately."
Klopp had seen his side concede an 85th-minute leveller to be held by Chelsea.
In-form Salah had handed the Reds the lead against his former club, as his fine form continues, but Willian’s late cross-shot rescued a point for the visitors.
Preserving squad harmony will be crucial for Klopp, with Mane a key figure in his plans.
Former England international Rio Ferdinand had suggested after Saturday’s stalemate that he felt there was more to an on-field spat than merely positioning on the pitch.
He told BT Sport: “He’s saying ‘let me play man’.
“It’s a showpiece. Big players, who has been producing over the past year for Liverpool, want to play.
“He wants to go out there and show how good he is and I think that’s his frustration there, from my eyes reading into that.”
While Klopp has sought to rubbish that suggestion, it remains to be seen what role Mane will play in Liverpool’s next fixture against Stoke on Wednesday.