Uefa is considering copying rugby's lead by allowing only captains to talk to referees during games.
In a Football Focus special report to be aired on BBC One on Saturday, Uefa's William Gaillard admits the current situation is becoming "dangerous".
He believes captains should take more liability for the game's direction.
"It's common in rugby to call both captains and say 'cut it out, the game is not taking the right course and it is up to you'," said Gaillard.
The Uefa spokesman also admitted that European football's governing body was concerned at the breakdown in relations between officials and players and managers, particularly when the disputes result in violence at amateur level.
"What is really worrying is what is happening in the lower leagues," he said.
"Retaining and recruiting referees is already difficult and without referees the game will descend into anarchy"
"That means the national associations can't find referees at the grass-roots level.
"If you don't find referees there, very soon you won't find referees for the lower divisions of the professional game and ultimately the elite (divisions)."
Gaillard disagreed, however, that the quality of refereeing had deteriorated.
He said it was the same as it had been for "a century and a half" and that errors were still rare.
Former international referee David Elleray agrees with Gaillard and points to the increased scrutiny that officials are under - thanks to television - as the cause of the heightened awareness of refereeing mistakes.
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He does not, however, think officials should be exempt from criticism if they make an error, as long as the criticism is measured and in context.
"I think it would be sad if we said that you can never comment on a decision or say a referee made a mistake," said Elleray.
"We comment on players making mistakes - for example, Saha missing the penalty (against Celtic on Tuesday).
"It was a crucial error but he didn't deliberately miss it, and it doesn't mean he is an incompetent player.
"But if the referee had made a similar error in that game there would be questions about his integrity, judgement and competence.
"It's what is behind the criticism, and the nature of the criticism, that is damaging for referees and football, not the criticism itself."
Elleray said that like Uefa he was concerned the current spate of high-profile rows following contentious refereeing decisions would hurt football.
"Retaining and recruiting referees at the grass-roots level is already difficult," he said.
"And without referees the game will descend into anarchy and chaos."
For more on this subject watch the full report on Football Focus on BBC One on Saturday at 1210 GMT.