Klopp said he deserved his red card for the way he confronted the assistant referee
Klopp was dismissed after berating a referee's assistant when a foul was not given for a challenge on Mohamed Salah.
The incident came on a weekend where Merseyside Youth League games were postponed amid ongoing issues with referee abuse.
Klopp apologised for his reaction in his post-match comments.
"Something snapped in that situation, I'm not proud of that. I deserved a red card, and the way I looked in this moment is not right," the German admitted.
Klopp has been charged with a breach of FA rule E3, which covers "comments which are improper, which bring the game into disrepute, which are threatening, abusive, indecent or insulting".
The 55-year-old has until Friday to respond to the charge and will be allowed to take his place in the dugout for Liverpool's home game against West Ham on Wednesday.
Following the win over City, Klopp said he went to see to referee Anthony Taylor and "spoke completely calmly" about how he felt the match unfolded.
He added: "The whole game led to that a little bit. It was a very, very intense game with a lot of decisions we didn't understand on both sides.
"This for me was like the one drop that made the bucket overflow. I'm not happy with my reaction but that's the way it was and everybody saw it."
Following Sunday's incident, a referees' charity called for an inquiry into the touchline behaviour of managers.
"People mimic what they see on TV," said Ref Support UK CEO Martin Cassidy.
"When you see world recognised figures behaving like that, it is then replicated by people in youth football and perpetuates the idea that it is OK to do it," he added.
-- Courtesy of BBC Sport