Referee Micheal Oliver awarded a free-kick for the incident but the Football Association have not deemed the episode worthy of further action.
The FA can take retrospective action for violent conduct and off-the-ball offences even if the officials fully observe the incident.
But Mane's actions have not been deemed serious enough to warrant an additional reprimand, meaning Jurgen Klopp will have him available to face City at the Etihad Stadium on Thursday.
Mane has scored nine goals in 25 appearances for the Premier League leaders, who are unbeaten in their opening 20 league matches of the campaign.
They lead Pep Guardiola's men by seven points ahead of their trip to Manchester but Klopp is unconcerned by the prospect of further increasing their advantage.
“We are [hungry],” he told the club's official website.
“We don’t think about the gap, not for a second. What we think about is 54 points – unbelievable, to be honest. That’s really strange and feels strange.
“All we can do is keep going; recover first of all, that’s very important, and then prepare the next game.
“We all know, wow, Man City are a fantastic football team and an away game at City – who can go there and think ‘Probably we will win’? No team in the world, not even us.
“So we have to go there and try everything to get a result. That’s what we will try.”