Klopp sprinted onto the field to celebrate Divock Origi’s late winner at Anfield.
He hugged goalkeeper Alisson before then dashing back to his dug-out to celebrate with the Liverpool coaching staff.
But Klopp has now been charged with misconduct for his actions.
He has until 6pm on Thursday to respond to the charge.
Jurgen Klopp apologised after the match, saying: “I have to apologise because I didn’t want to be disrespectful – but I couldn’t stop myself.
“If I could describe how I felt when the goal went in, then I would have control over it. We don’t want to look for excuses but that’s how it is.
“The plan was not to run. When I chose to stop, I was close to Alisson. He was surprised.”
And the FA’s decision to charge the Reds manager has annoyed their fans.
“No passion in football anymore he apologised & also Everton’s own manager would have done the same if it happened to him,” one fan wrote.
Another put: “Klopp wasn’t disrespectful telling the Everton fans to *shush* and he celebrated with the player who kept us in the game.”
And Klopp has garnered support from fans of other clubs.
An Arsenal fan wrote: “If the media darling pep would have done that it would be ok but if klopp or Jose do it is frowned upon, double standards.”
A Manchester United supporter wrote: “The FA are bloody sad charging Klopp with misconduct after celebrating the win against Everton ! @FA need to get a life ! The game has gone to soft !”
And a Crystal Palace fan wrote: “So Klopp has been charged for showing passion ?? What a joke and I am a Palace fan before you all have a go lol”
A Brighton support chipped in and said: “That’s right, take the passion and individuality out of the game. I’m not a Liverpool supporter but seeing Klopp run across the pitch shows how much he cares for his club”
And a Rangers fan said: “Absolutely ludicrous-the lawmakers obviously haven’t played football to any extent-it’s a passionate sport -emotions get very high -Klopp was just on a high after getting a winning goal in such dramatic fashion.”
A Manchester City supporter joked: “Hahah Klopp have been saving this celebration for last season’s Champions League Final clash, but he didn’t get to.”
