The Scotland international let in Badr El Kaddouri's tame shot on the stroke of half-time to hand a 2-1 lead to the Hoops before his 'Gers teammates rallied to eventually record a 4-2 victory at Ibrox.
McCoist says that McGregor has a strong enough character to not let a mistake like that affect him and will be back to his best in no time.
"Allan is a strong character, really strong, as strong as any of the boys I've played with or been involved with," McCoist said.
"His desire to work hard in training, not lose goals in training or goals in games is up there with anybody.
"He's had a few slip-ups. But he's got a great belief in himself which, especially for a keeper is, if not a necessity, is damn near it.
"You think of all the great keepers, they've all been really strong characters and Allan would come into that category.
"He also has more to deal with from fans than the majority of players but believe me, they're wasting their time. It's like petrol to him, it gets him going. He thrives on it.
"He doesn't go out of his way to wind people up but he's one of these characters that attract some of it.
"The vast majority of it is unfair criticism from opposing fans but that's football.
"And as I would say to anybody who does get that reaction - you must be doing something right. There are not too many bad players get stick from opposing fans."