Bruno Fernandes angrily remonstrated with Victor Lindelof after Luuk De Jong put Sevilla ahead in Sunday's Europa League semi-final in Lisbon.
The Portuguese midfielder has been a revelation at Old Trafford since joining in January, however, John Giles feels that his criticism of the central defender could have taken place after the game.
It could have a negative effect on Manchester United's morale in the long-term, according to Giles.
"It's not good and even in the dressing room, the manager should be saying that," the former United midfielder said.
"Players can take too much on themselves and he did that on the pitch as well and everyone could see."
"That should not happen in a team because next week he could go and have a nightmare, Fernandes, maybe miss a penalty, maybe miss a couple of chances. Does Lindelof go up to him and say 'what the hell are you doing?"
"That's what breeds bad team spirit. You should keep your mouth shut in those situations until you get into the dressing room. It looks terrible on the pitch when one colleague gets onto another colleague."
Despite having a number of chances to kill the game United were undone by De Jong's late winner.
There were a number of mistakes made by various defenders in the lead up to Sevilla's goals and Giles feels United did not perform well in any of their European games after the lockdown.
"I don't think they've played well in this competition. To be fair the goalkeeper [Yassine Bounou] for Sevilla played really well and they could have scored more goals than they did, but they shouldn't have conceded the goals that they did."
After going behind Ole Gunnar Solskjaer's men never really looked like they would find an equaliser and Fernandes and Lindelof's interaction did not help.
The fact that there are numerous cameras beaming the images worldwide does not help the situation, even so, Giles made the point that he never publicly dressed down a team-mate during his time at United or at Leeds.
"I had a policy when I was playing, never to say anything that the public could see, to a colleague. I'd have a go at Eddie Gray but I'd be near him on the pitch. I'd say come on Eddie you shoud not be doing that but nobody else knew that."