Rival bosses Nigel Davies and Mike Ford were both critical of the officials after a spiteful Aviva Premiership West Country derby between Gloucester and Bath at Kingsholm.
Gloucester ended the game with 11 players after Sila Puafisi and Tavis Knoyle were sent off and Mike Tindall and Huia Edmonds were sin-binned.
Bath also had three players yellow-carded before claiming an 18-17 victory thanks to a converted 79th-minute penalty try, while a second-half decision by referee Tim Wigglesworth to go to uncontested scrums also sparked controversy.
And Wigglesworth appeared to have a plastic drinks bottle thrown in his direction as he walked down the players' tunnel after being escorted off the pitch at the end of an ill-tempered contest.
A Rugby Football Union spokesperson said on Saturday the match would be "subject to a full review by the RFU, as per normal procedure".
Asked if he thought there should be an enquiry into the game’s events, Bath head coach Ford said: "I think so. We've had four yellow cards all year and we got three in one game. Derby games are very passionate and players get on the edge.
"We pride ourselves on these challenges that occur during a game. We try and pride ourselves on figuring a way to win and understanding what is going on.
"The referees have got to understand what is going on out there. It's crucial, absolutely crucial. Why he never used the TMO (television match official), I don't know.
"I am not here to call the referee at all, honestly. I just want to be positive on what we have done."
Ford also had some strong words for Wales international Knoyle, who was dismissed after he threw punches at Bath No 8 Leroy Houston in the dying stages of the game.
He added: "What happened at the end with Tavis Knoyle, there is no place for that. He just assaulted one of our players. We've got to defend ourselves. You can lose control, can't you?”
"There were a lot of controversies during the game. We had to deal with it and the players and the decision-making on the field was fantastic.
"We are really pleased to come through a very hostile, ferocious Kingsholm and keep in the top four of the Premiership."
Bath were also furious that the game went to uncontested scrums, with Wigglesworth making that decision because Gloucester said one of their replacement props - former London Irish player Dan Murphy - could not play in the tighthead position.
"We've got two coaches on our coaching staff who've coached him. It took a massive part of our game away. It's just not right,” Ford said.
"Health and safety comes first. I am not too sure the last time he played tighthead or not, but uncontested scrums are no good for the game."
Gloucester director of rugby Davies insisted Murphy is not trained to play tighthead and said staying with contested scrums with him in that position would be “absolute madness and dangerous”.
Davies was also unhappy with the standard of the officiating, saying the decisions were not consistent throughout the game.
He said: "I think right from the start of the game the lack of consistency shown really frustrated a lot of players from both sides. When it is not managed and there is no consistency, you are going to get frustration.
"The players work very hard to put stuff together and be the best that they can be, and when there is a lack of consistency it is very difficult."