Both managers and their benches were forced apart by police and stewards as the clash threatened to get out of control in the closing stages, with Tykes boss Simon Davey infuriated by the multi-ball system employed at Bramall Lane.
The incident was mentioned in Hertfordshire referee Grant Hegley's report and the FA confirmed they are examining video evidence to determine if any sanctions will be employed against either club or any individual.
Both Davey and Blades counterpart Kevin Blackwell played down the confrontation and were seen to embrace at full-time.
"It was nothing really," said Davey. "I was disappointed with the multi-ball system. That was the issue.
"When Sheffield United scored their first goal all the balls disappeared. We had 24 when we were drawing and then there's one ball in the stadium when we're losing the game.
"I spoke to the referee and there were words exchanged, but it's nothing."
Blackwell, who refused to comment on the police's intervention, said: "I don't control the multi-ball system and it never went missing. I don't know what he's on about."