The Light Blues looked set to extend their lead at the top of the Irn-Bru Third Division to 22 points thanks to a John Crawford own-goal.
But they were left reeling when David Gray came off the bench to snatch a share of the points with a minute to go with a superb long-range effort.
As well as the 1-1 result, McCoist was furious with the performance of his lacklustre players, who left the pitch to the sound of jeers from the home support.
The Gers boss said: "I was booing myself. I'm probably as angry as I've ever been as manager with that performance.
"I'm not even interested in the wonder goal with a couple of minutes to go. You could see it coming, you could absolutely see it coming.
"Our overall performance was not good enough and our standard of finishing was probably worse."
Asked if his players switching off was the problem, McCoist said: "I don't know. But I tell you what, they better switch on kind of quick or they will be completely switched off.
"What I'm saying is, that level of performance can't, and won't, be tolerated.
"It seems a bit bizarre saying that when they've only had two draws in 14 games but, at the same time, the supporters deserve a better level of performance than what they got today."
McCoist was unwilling to use the absence of injured skipper Lee McCulloch as an excuse for the poor display.
"It's too simple to say that," he said. "That team we put out there today, regardless of the result, should be performing at a higher standard."
The result comes just a week before Rangers face one of their toughest games of the season when they travel to Dundee United in the William Hill Scottish Cup.
McCoist said: "Not just because of today, but United will be strong favourites. That isn't attempted mind games or anything like that, it's just an honest opinion.
"I would hope that today's level of performance would act as a wake-up call to not even one or two but a lot of the players.
"I said my piece after the game but we do live and die as a team and that will always be the case."
A disappointing day was compounded by the sight of Lewis Macleod leaving the pitch on a stretcher, before Chris Hegarty hobbled out of the action.
McCoist said: "Lewis is in a bit of pain. We will have a look at him tomorrow.
"It's his knee. We will have a better idea of how he is tomorrow.
"Chris Hegarty came off with the similar thing he had against Berwick, some cramp forming in his thighs.
"If it's something the doc has to have a look at, he will have to have a look at it."
Asked if he regarded the result at Ibrox as a shock, Montrose boss Stuart Garden said: "Everybody will do.
"Not many teams get points here. It is very hard because they are a good quality side.
"But we've been doing well recently and we came down here hoping to get something."
