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Speaking to the media after the game, both managers were reluctant to comment on the behaviour of supporters.
"As we were making our way back, I think there was some sort of fracas; somebody tried to get on the field," Celtic interim boss Martin O'Neill said of the fan who wrestled with a member of his staff.
"And as you say, maybe it does taint proceedings, but I think there's an element of self-protection in that one. So if that's the case, please, I'm making judgments here on things that I only half saw.
"The security men, in fairness to them, were wanting to get people off. But there is a natural euphoria about winning a game and about fans joining in. If this has gone too far, that would be disappointing."
Rangers head coach Danny Rohl insisted he did not see the trouble.
"I was not on the pitch in this moment. I didn't see it until now," the German said.
"Nobody likes to see this. It was a great atmosphere in 120 minutes. All the other things should not be in the stadium or around football."
Speaking on Monday, Scotland's first minister John Swinney said the violence has no place in football, calling it "completely unacceptable".
"The violence after the Old Firm game yesterday at Ibrox was completely and utterly unacceptable – there is no justification for it whatsoever," he said.
"There was severe danger applied to fans and to police officers and to stewards, it was completely unacceptable in every respect.
"What I want to make clear is the police have my full support in pursuing everyone involved in this incident, also that we will work constructively with the clubs - who must be horrified by the scenes that they witnessed - as well to address the situation, to work with the Scottish Football Association, to make sure that collaboratively and collectively, we do all that we can to make sure that these types of incidents have no place in Scottish football."
Former Celtic striker Chris Sutton also criticised the "ugly" scenes.
"When a fan comes on to the pitch, they know they shouldn't be doing that," he said on BBC Radio 5 Live.
"We understand the emotional side of the game - Celtic have beaten their biggest rivals at Ibrox.
"It was really ugly. It's shameful for the game up there. It's sad because the full allocation is what you want.
"What happened today shamed the game north of the border."
