After Dejan Kulusevski had headed a late leveller to peg City back at the Etihad Stadium, the hosts thought they were set for a huge opportunity to win a thrilling game.
Erling Haaland was tripped in the centre circle but quickly rose to his feet and a ball over the top found Jack Grealish to run through on goal, however referee Simon Hooper blew his whistle to bring the play back for the foul on Haaland.
That led to a furious response from the Norwegian striker, plus several teammates, who surrounded Hooper to argue that he should have played the advantage and allowed Grealish to continue his attack.
On Monday, the FA announced a charge with a breach of Rule E20.1 for the club "failing to ensure their players did not behave in a way which is improper".
City have until Thursday, December 7 to respond.
The Premier League champions face a fine if found guilty.
Hooper, 41, has faced criticism for his failure to play advantage but will not be stood down from refereeing in this coming midweek's round of matches. He will referee Sheffield United vs Liverpool at Bramall Lane.
The official found an ally in ex-referee Dermot Gallagher after City's draw with Tottenham, who said he did not technically go against the rulebook but did make the wrong call on this occasion.
"It's the referee's choice to play advantage, not anybody else's. In law he hasn't done anything wrong."
Dermot Gallagher talks us through Simon Hooper's decision to not play advantage for Man City. pic.twitter.com/UQdvNGqbOX
— Sky Sports Premier League (@SkySportsPL) December 4, 2023
He told Sky Sports: "It's the referee's choice to play advantage - nobody else's - so by the law he has not done anything wrong. It's just how we apply the law."
Gallagher added: "It's difficult, because this is a lad who I'd say plays more advantage than anybody else normally. He lets it go and lets it go and takes a long time to bring it back and, sometimes, he's on the cusp.
"You see quite rightly he plays on and you can see why. The ball goes to Grealish and he's away and, for whatever reason, Simon puts his whistle to his mouth and blows it.
"We spoke a few weeks ago about referees being like players, the best players delay things a little bit. If he'd have waited one second the whole landscape changes but, unfortunately, he didn't. It's unfortunate, but it's just an error that he's made."