The Senegal global was surprisingly benched for the match at Anfield and was only brought on with one minute remaining.
Alex Oxlade-Chamberlain and Daniel Sturridge began the match in their place and the former assisted Mohamed Salah for Liverpool's opening goal in the second half.
The Senegal global was visibly upset with Klopp at the end of the match with the Liverpool boss claiming it was due to an on-field disagreement the pair had.
The 25-year-old was able to play 74 minutes in the 3-0 win over Southampton last weekend and followed that up with a full game in the 3-3 draw against Sevilla on Tuesday evening.
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Senegal worldwide Mane, who has scored three goals from eight Premier League appearances this season, was surprisingly demoted to the bench for the encounter against defending champions Chelsea.
"So, that's good for keeping the team strong and, as I said, we've got players coming back from injuries like Adam among others".
'He said to me that Mo [Salah] wanted to come into the position but Mo had 90 minutes in his legs.
"I wanted to sort it out immediately".
"So it would have made more sense that Sadio was close to the right-wing and started 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".