The game was always keenly fought and ended with skirmishes on the pitch, which apparently continued as the players departed from the public view.
Celtic manager Strachan told BBC Radio Scotland: "I've not got a clue what happened.
"For me to comment on something I don't know anything about, would be like me talking about politics. I never saw anything there."
Asked if the referee requested to talk to any Hoops stars, Strachan said: "I think he wanted to speak to one or two players after the game. I think he spoke to one or two players."
Rangers boss Walter Smith insisted he was unaware of post-match trouble involving the players and had no comment on the flare-up on the pitch.
"I was coming up the tunnel. I don't know," said Smith.
"You look at the two teams who are committed and these type of things will happen.
"I think you'll notice I shake hands with the opposition manager and leave.
Strachan felt his side were worthy winners but at one stage he feared Scott McDonald's missed penalty, which followed a red card for Carlos Cuellar for handling on the line midway through the second half, would cost Celtic dear.
"I know we deserved a result but the football gods have not been kind to us recently," Strachan told Setanta 1. "I thought we played very well tonight.
"It's great to beat a Rangers team that's been so consistent, so professional and doing so well this year."
Of the penalty miss, he said: "It says a lot for the lads to take the body blows that they had and to come back and win."
On the title race, he added: "It's just nice to win an Old Firm game. It's got nothing to do with the permutations after that.
"We're now looking like we can score goals again, which is good."
Hoops striker Jan Vennegoor of Hesselink insists Celtic had earned their good fortune after he scored the winning goal in the third minute of injury-time to end Rangers' unbeaten domestic run, which stretched back to October.
Shunsuke Nakamura put the Hoops ahead with a spectacular, swerving shot from 25 yards after 20 minutes.
Substitute Nacho Novo drew Rangers level when he finished well from an angle.
The penalty save followed and the game appeared to be heading for a draw before Vennegor of Hesselink's late intervention.
The result means Celtic close to one point behind Rangers in the SPL although the Gers have two games in hand.
Vennegoor of Hesselink told Setanta 1: "The result was very good for us. One-nil in front you think you are in control, then they score a goal, but you score in the last minute. It's great for the team.
"It was like Ibrox (where Celtic lost 1-0), but it didn't go for us. Today maybe we had a bit of luck in the end but I think we deserved it.
"(I thought we must) go on and try and score another because they were with 10 men. It may be last minute but it can be sweeter.
"The gap is still there but I think they can feel the pressure a little bit."
