Cole was shown just a yellow card by referee Andrew Dallas despite catching Frimpong on the knee in a studs-up challenge in the second half.
Frimpong limped on for a bit but ultimately had to be substituted for Hatem Elhamed, who would provide the cross for Mohamed Elyounoussi to complete his hat-trick as Neil Lennon’s men returned to winning ways in style following Thursday’s Europa League humbling against Sparta Prague.
Celtic must now wait to hear the full extent of the damage Frimpong suffered with his manager fearing the 19-year-old has sustained ligament damage.
While that would be a significant blow for both the player and Celtic, Gallagher reckons it could have been a lot worse if the right-back had his leg planted when Cole made contact.
Speaking on Sky Sports, the ex-whistler stated his opinion that Dallas got the call wrong.
He said: "I think both players are extremely lucky. I think Cole is lucky he didn't get a red card because the point of contact is really, really bad. And I think Frimpong is lucky he didn't suffer a serious injury. If his leg is planted, that's a very dangerous tackle.
"I just think the referee has read it wrong."
Motherwell manager Stephen Robinson, meanwhile, insisted it wasn’t a red card offence because Cole didn’t show any “malice” in the challenge.