The two benches had to be separated by police and stewards after words were exchanged after Daniel Bogdanovic had pulled a goal back for the Reds in the 90th minute.
Davey claimed to have been upset at the disappearance of the multi-ball system after the Blades took the lead. He said:
"It was nothing really. 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."
His counterpart, Kevin Blackwell said: "I don't control the multi-ball system and it never went missing. I don't know what he's on about."