Video footage appeared to suggest the Hull substitute spat in Hart's direction after the goalkeeper had reacted furiously to Boyd's fall under his challenge in the box in the 69th minute, although Tigers manager Steve Bruce denied that was the case.
Referee Lee Mason booked Hart for his part in the incident with Boyd, who later added to the controversy by insisting Hart "put his head in" and should have been sent off.
The FA will await the referee's report on Monday before deciding whether to take any further action over the incident, which soured a fine win for a City side who had been reduced to 10 men in the 10th minute after captain Vincent Kompany was dismissed. The Belgian may also face further punishment for his reaction to being sent off.
David Silva put the visitors ahead with a delicious left-foot strike four minutes later, then Edin Dzeko wrapped up victory after being put through by Yaya Toure in injury time.
Bruce defended Boyd over the spitting allegation, describing it as "a load of rubbish" and adding: "He (Boyd) has tried to talk and shout and something's come out. That's what I've seen of it.
"George Boyd wouldn't do that, no chance. Not deliberately, anyway. He is as honest as they come - he was playing non-league six years ago."
Bruce also backed Boyd over the suggestions of diving, accepting referee Lee Mason got it right in not awarding a spot-kick but adding: "George has tried to go round the goalkeeper and he has lost his balance.
"Boyd is going at full tilt and he's expecting to get clattered. To be fair to Joe he has done what every experienced goalkeeper does - he's pulled himself out of the road. George is trying to take evasive action rather than simulate to get a penalty."
Meanwhile Boyd, who was at the centre of another, arguably stronger penalty call when he fell under Fernandinho's challenge two minutes later, criticised Hart's reaction to the initial incident.
Boyd said: "He didn't nut me but he's put his head in, so he should have got sent off really.
"He said after he didn't touch me, but I thought he touched me a little bit. He came (after the game) and said he didn't touch me. He apologised for the reaction and that's it."
The controversy took the shine off a solid City performance, which was later given new importance after title rivals Chelsea slumped to defeat at Aston Villa.
The weekend results mean City now trail Jose Mourinho's men by six points, but with three games in hand they now have their destiny back in their own hands.
Midfielder Samir Nasri said: "Sometimes you can win games when you are lucky and that can make you a champion. We know if we win our last 11 games we are going to be champions."
Nasri criticised the dismissal of Kompany, insisting the City defender had been fouled by Hull striker Nikica Jelavic first, but said the sending-off had helped instil a new motivation within his team.
Nasri added: "When everyone plays for the team it doesn't matter if we have 10 or 11 - we can win games because we have quality.
"It was a mistake from an official because the first foul was on Vinnie and he took a red card, so for 80 minutes we played with 10 men.
"When your captain gets a red card you just want to show that you can do it without him and as well for him.
"It was up to us to continue to run and defend the way we did with 10 men. You want to fight to the end and that's what we did."