Celtic manager Neil Lennon and Dundee United boss Jackie McNamara both accused opposition players of "reckless" tackling after a Tannadice clash that was settled by Anthony Stokes' late free-kick.
Lennon took aim at United's Gavin Gunning, while McNamara was critical of Scott Brown.
Celtic defender Mikael Lustig was carried off on a stretcher early in the second half after appearing to fall awkwardly following a hefty challenge by defender Gunning.
Lennon said: "I thought the challenge on Mikael was reckless to say the least.
"There is no fracture thankfully, it might be ligament damage. It is a relief because he is a top player."
Gunning denied the accusation, saying: "I didn't think there was much in it, we both just went for the ball and I landed on top of him but there was no malice in it. I went in after the game and he was okay, so it couldn't have been that bad."
Frustrated United manager McNamara pitched in on the issue by saying: "I think he went for the ball and they came together.
"I think a reckless challenge would be Scott Brown on Stuart Armstrong, I would say that was reckless."
The game looked to be drifting towards a draw when Stokes went to ground after going past Stuart Armstrong on the edge of the box.
The Irishman curled the 87th-minute free-kick over the wall and past Radoslaw Cierzniak, with the ball going in off the post, although United complained that the Celtic player had moved the ball back to give him an advantage.