An early goal by Brian Allison was enough to earn victory for Stirling and ensure that Rangers are still without an away league win this season.
While McCoist insisted that he did not feel under any more pressure than usual, he acknowledged his managerial ability would be called into question after what was their first league defeat of the campaign.
“Obviously, it goes with the territory,” he said. “Nobody needs to remind me of what is required from any manager, and that is results. And today, we lost a league game, which I am sore about. I’m extremely disappointed, exasperated, but it is not a real shock, given our away performances.”
While Rangers, who are third, have performed well enough at Ibrox, they have lost one and drawn three of their four away league games.
Asked to explain, McCoist said: “I am at a loss, I have to say. I would eradicate the problem if it was evident. I don’t think you need to be a top coach to see that we are not the same team away from home as we are at home. But there is a determination to put it right, and we will.”