The two players clashed during a fraught encounter at the KC Stadium, which 10-Man City won 2-0 with goals from David Silva and Edin Dzeko after Vincent Kompany had been dismissed for hauling down Nikica Jelavic after just 10 minutes.
Hart squared up to Boyd after he went down in the penalty area, with the England international accusing the Hull striker of diving.
The pair were separated following a heated exchange, and both players were defended by their respective managers.
City coach Manuel Pellegrini reckoned Hart must have had a good reason for confronting Boyd.
Pellegrini said: "For my position it was very difficult to see it because it was far away from my bench.
"If Joe reacts maybe the other player dived. I don't know."
But Hull boss Steve Bruce insisted his player did not dive.
Bruce said: "There's a difference between simulation, diving, cheating, if you like, than trying to get out the road, and that's what Boyd's trying to do.
"I mean nobody's going to stand there with Joe Hart hurtling at you. He's going to try and get out the road which he tried to get out the road, stay on his feet and keep the ball in play."