Hibs host Heart of Midlothian at Easter Road on Sunday and the 30-year old defender wants to avoid the circus that came with a recent meeting between Celtic and Rangers where everybody with an opinion seemed to get drawn in.
"We don't want to end up in the same scenario as the Old Firm a couple of weeks ago, when police, politicians and everyone got involved," Murray told SunSport.
"Thankfully, through in Edinburgh we seem to have a lid on that at the moment. Hopefully that will continue.
"I do think the Old Firm was blown out of proportion, completely and utterly, because it was the Old Firm.
"Through here in Edinburgh, I don't think anybody really cared, as long as nobody's getting killed.
"But I think you have to take heed. I think every footballer has to now, because you can't do something on the field that you wouldn't get away with in the street, realistically.
"If you go and punch someone in the face then, yeah, you should probably be reprimanded by the police.
"There is pressure on the police to react now if they see something.
"Yes you'll get the odd bad tackle, and that's fair enough, that has to be in football or the game will change.
"But what we don't want is people spitting on people, punching, head-butting people.
"You will go to jail at the end of the day."