The visitors had twice taken the lead at Ibrox through goals by Sean Dickson and Sean Higgins either side of a Nicky Law strike for the home side.
Fraser Aird's strike - which deflected in off Ross McMillan - and a Jon Daly header looked to have spared Rangers' blushes, until Higgins converted from the spot after Emilson Cribari was penalised for a pull in the box.
McCoist's side have now failed to keep a clean sheet in their last three home fixtures, and the Ibrox manager was disappointed in the manner in which his team defended.
"The first two goals are disappointing," he said.
"The first one we could have stopped the ball at source before the cross came in. I thought Temps (David Templeton) and Waldo (Lee Wallace) should probably have handled it better and certainly when the cross came in, Sebastien (Faure) should have handled it better.
"The second goal, I think Waldo went by Temps and we lost the ball and the cross came in. It was a good header I've got to say, from Stenny's point of view it's a great goal. So there were two disappointing goals, and then the penalty."
Rangers' tendency to concede at home is at odds with their form on the road, where they have picked up eight clean sheets in a row on league duty.
"I just think perhaps teams are countering us a little bit," said McCoist.
"Obviously in their own grounds they are probably under a little bit of pressure to come at us a little bit more, being their home fixture.
"We're possibly getting caught out of position when we are going searching for goals at home, so it's something obviously we have to look at."
Templeton had a day to forget for Rangers, the winger being cautioned for simulation after referee Greg Aitken ruled him to have gone to ground too easily in search of a penalty, before missing a glorious open-goal opportunity to settle Rangers' nerves.
McCoist said: "It was certainly a chance. I was extremely surprised and obviously disappointed, but listen, it happens.
"I've been known to miss one or two myself, maybe not just like that, but I certainly missed one or two myself.
"I'm in no way, shape or form singling Temps out for us not being good enough to win the game, the biggest disappointment was that after scoring three goals, we came away with one point and lost three goals."
There was at least some positive news for McCoist regarding the fitness of defender Faure, who was carried off on a stretcher just before half-time following a 50/50 collision with Kevin McKinlay.
"He's fine, he's back from the hospital," McCoist said.
"He went for an X-ray, he's just got a really sore one all the way down his shin and his ankle, but thankfully there are no breaks, no fractures.
"As sore as it, he'll be fine and he'll recover okay."
With new Stenhousemuir manager Scott Booth not taking charge of team affairs until March, interim manager Brown Ferguson was understandably delighted with his side's showing, particularly on the back of a wretched run of form that sees them still searching for their first win of 2014.
He is now hoping this result can kick-start their season.
"What we basically were saying to our players is that there's a level of consistency and concentration required," Ferguson said.
"There's a reason why players are playing at our level. There are a lot of good players in that changing room, and if they can keep up their level of performance week in, week out, then they can go on and do better things."