The SFA compliance officer is reportedly reviewing footage of the match, which Hearts won 1-0, with home attacker Steven Naismith and Celtic’s captain Scott Brown in danger of being cited.
Naismith had a kick out at Jonny Hayes as the two lay on the deck following a challenge by the Irishman.
Brown, meanwhile, appeared to catch Naismith with his arm as he looked to shield the ball from his opponent.
Gallagher, appearing on Sky Sports News, felt that neither incident should be punished with a retrospective red card.
With regards to the Naismith kick out, he said: “I don’t want to be knee-jerk because it’s so easy to say stamp or such like.
“He feels aggrieved because Hayes has knocked him down.
“He has a little flick out and what is almost a brush with his studs, to me. It’s not malicious, it’s petulant.
“For me, it’s not worth a red card. It’s not a wise thing to do.”
On Brown’s clash with Naismith, he said: “Again, you always run the risk. But it’s hardly an elbow. It’s a flailing arm.
“His arm has come up and we have to be careful that we do go gung ho and start lashing yellow and red cards about.”