The Gers went down 1-0 to Tommy McIntyre's side at Parkhead as Aidan Nesbitt netted the only goal of the game in front of a crowd of around 8000.
Smokebombs and flares were set off as the Old Firm fans made the most of their chances to renew past rivalries while seats were broken in the Rangers end at the final whistle.
The Light Blues almost snatched a late equaliser when Sam Jamieson struck the bar in injury-time but it was their Glasgow foes who would claim the spoils in a manic atmosphere.
Boss Kirkwood said: "We are only focusing, as the players are focusing, on the game.
"What happens on the terracing, we can do nothing about that. Unfortunately, you guys [the press] were sitting round about it. Unfortunately, it is just society at the moment.
"I thought it was a good game and two contrasting styles with both teams trying to win it in their own fashion.
"Unfortunately these things happen off the pitch. That is probably a bigger picture.
"It is not just Rangers and Celtic, it is society in general.
"How you combat that? I wish I had a magic wand.
"As we said last year, there will be a time when Rangers and Celtic are going to play together at first-team level."