Brown was involved in the incidents that led to red cards for Alfredo Morelos and Andy Halliday plus a potential two-match ban for Ryan Kent.

Players' behaviour in the Old Firm game was labelled "unacceptable" by a senior Scottish police figure.

"I don't think Scott did anything wrong," McGregor said.

Brown was elbowed by Morelos after clipping the Colombian's heels. Kent later lashed out with a shove when Brown delayed Rangers' kick-off after Celtic's winner in the 2-1 victory.

The Celtic captain's post-match celebrations in front of the away support led to a confrontation with Halliday and mass fracas.

Rangers manager Steven Gerrard claimed Brown "antagonised" his players and should be punished.

"These wee tactical, mind games, whatever you want to call them, are part of football," McGregor said.

"That's nothing for anyone to speak about Scott and his behaviour, it's obviously the other side. With the Morelos one, he runs across the path of him and gets that reaction. It didn't warrant that."

Scottish Police Federation vice-chairman David Hamilton spoke out on Monday to criticise the players' behaviour in the derby, which also included a pitch invasion from some Celtic fans and flares being thrown.

"I don't think we did a huge amount wrong," said McGregor. "We won the game and inside your own stadium you're entitled to celebrate.

"There's obviously been a few flashpoints, but it's hard for the players to take responsibility for what happens outside the stadium. We're role models, but we can't control everything."

Morelos's red card was his fifth dismissal of the season, one of which was rescinded, and McGregor admits the Celtic players were well aware of the 22-year-old's temperament.

"You can see his record over the season," McGregor added. "If people provoke him, try to get in his head, he's going to react and I don't think it's any different in a big game for us. We're always trying to get the edge. If you can provoke people or do things to get an advantage it's fair game.

"It was never a specific tactic. But players understand what they see in other games and they are not stupid, they know how to win."