But Robins chairman Paul Baker has warned the Town boss not to repeat such behaviour in the future.
Yates issued a public apology on Sunday for the use of bad language aimed at a supporter immediately after the promotion-chasing club's disappointing defeat at Home Park.
The fan in question had singled out substitute Kaid Mohamed for strong criticism at the end of the game.
Baker told the Gloucestershire Echo: "It was an abysmal performance at Plymouth and I think we probably all felt like swearing, but Mark should not have said what he said.
"We have mentioned it to him and stressed to him that he must try to bite his tongue in those sorts of situations in future.
"We are all human and it was a heat of the moment thing so I do not envisage any action being taken.
"It shows Mark's passion and that is essential for a manager to have, but it's all about ensuring that is pointed in the right direction.
"It's been a great season to this point and we want to put this incident behind us now and look forward to Saturday's match."