Grimsby manager Paul Hurst indicated Stefan Payne may not play for his side again this season after he was sent off for head-butting team-mate Filipe Morais in Saturday's defeat at Bradford.
Soon after Anthony O'Connor had put Bradford ahead the two players were seen arguing as they headed towards the tunnel at the end of the first-half, with Payne then leaning in to head-butt the veteran midfielder.
Referee James Bell saw the clash between the two players and quickly took out the red card, though he had to follow Payne into the tunnel in order to show it.
Grimsby's Twitter account described the incident as "unforgivable", and Hurst – who withdrew Morais at the break – was still angry about it after the final whistle.
"It is something you can't defend," he said. "The two players have let the club down, the pair of them. They have let their team-mates down and the fans down.
"As far as the game is concerned they made it more difficult than it needed to be. I didn't see it because I was making my way down the tunnel, but clearly it merited more than being a little spat.
"Now I have to concentrate on what to do next for the good of the team. The club will be taking action. That will remain private but it won't swept under the carpet.
"(Payne) will get a three-match ban for being sent off, but I have got some thinking to do before I decide whether he plays again for the club before the end of the season."
The defeat ended Grimsby's eight-match unbeaten run and left them rooted to the bottom of League Two, seven points adrift of safety with six games left.
