The Light Blues had led at half-time through Barrie McKay but the Blue Toon were in line for a shock victory when they turned the match on its head.
Rory McAllister and Scott McLaughlin’s goals had the Buchan outfit on the verge of a sensational win in Gers’ first ever league match outwith Scotland’s top flight.
But Andy Little rescued the visitors in the dying seconds when he bundled the ball over the line after Kevin Kyle’s header had hit the bar.
Regardless of their escape, manager McCoist was furious at the manner of his team’s showing and he’s looking for a massive improvement.
He said: “I’ve just said in the dressing room to the players that if any of them just thought it would be a cakewalk they are mistaken.
“If they thought they could just turn up, take three points and that people would let them get on with it, that’s a rude awakening they’ve got. If it’s a lesson learned today, we’ll take it.
“That was a battle and the one thing you have to do in any game of football is earn the right to win. I don’t think we did that in the second half today.
“We have to show our calmness, take our time and put our foot on the ball. Peterhead didn’t just sit back – they played the ball longer and put our back three under immense pressure.”
McCoist was particularly angry with the way his team defended as it conceded two sloppy goals and struggled to deal with the pressure it was put under.
He knows his team had enough quality to win and was frustrated that it had to scrap for a point instead.
The manager added: “I don’t think there’s any doubt we should have won and again, we missed an incredible amount of chances.
“We can’t get away from the fact that we didn’t defend well enough. We defended extremely poorly and we were punished for that.
“With five minutes to go, I would have been more than happy with a draw and we’ll have to play a lot better than that.
“We weren’t anything like as crisp as we were on Tuesday with our passing and we didn’t handle Martin Bavidge’s physical presence at all well.
“Our defending all day, but particularly in the second half, wasn’t nearly as good as it should have been.”