The Rangers goalkeeper was at fault for Elgin's late equaliser, fumbling the ball into his own net following a Jamie Duff header, but the home fans left in the main stand still applauded him as he walked up the tunnel.
They did the same for the Elgin players as they departed in jubilation, but there had been derision moments before when the final whistle was blown. Rangers only had themselves to blame, after all, for dropping two points in a game that they commanded.
The glaring error was Alexander's, since he had dealt with Duff's header by parrying the ball, only to then mishandle and send it backwards into the goal. Yet the rest of the players were culpable for the failure to capitalise on their dominance.
Elgin were reduced to 10 men late in the first half when Paul Harkins was sent off for raising his foot when he challenged Ian Black for the ball, but the visitors had already been constrained.
Rangers ought to have won this game comfortably, but they were indecisive and careless in the final third, which eventually cost them the first points they have dropped since October, and their first at Ibrox all season.
"We should have been out of sight, but that said, we didn't play well," McCoist admitted. "I said to the boys at half-time, the longer it's 1-0, the more likely they'll get a chance from a free kick. We gave away a silly free kick, defended it appallingly, and it was a comical goal to lose eventually. Neil's big enough to recover from it. He knows he made a mistake. But there's an argument that we got what we deserved in a game we should have won."
Rangers had eased into control of this encounter. There was resistance from the visitors, at least in defence, but Elgin only sporadically broke upfield on the counter-attack.
Alexander almost miscued one clearance under pressure inside his own penalty area, and comfortably saved a Sean Crighton header following a rare Elgin corner kick, but otherwise the goalkeeper barely participated in the opening half. The home side could revel in their dominance of the ball, particularly after Lewis MacLeod opened the scoring in the ninth minute, but Rangers' control of the game at times seemed more of a burden, as if it were a trial.
Elgin packed their defence, for instance, forcing the home side to try to squeeze the ball through tight gaps to try to force an opening. The onus fell on the creative players to ensure that the scoreline reflected the nature of the contest.
MacLeod was prominent in that regard, since he was playing a central attacking midfield role. He tended to be involved in the best of Rangers' first-half play, and the goal was a reward for his tenacity as much as his ability. He sidestepped two weak challenges as he skipped across the penalty area before hitting a low left-foot shot beyond Joe Malin, the Elgin goalkeeper.
The visitors must have feared a dispiriting day, but much of Rangers' work took place outside the Elgin penalty area and they seldom managed to move the ball in behind the defence.
When Malin was called upon, he produced an excellent save at close range from Lee McCulloch. By then, Elgin had been reduced to 10 men, and the game plan at half-time was to survive the encounter.
"I thought we were in for a bit of a doing," said Ross Jack, the Elgin manager. "But we knew if we got a free kick or a corner we might just nick something, and that's what happened. They showed some character and I'm proud of them.
"I'm not embarrassed saying that we sat back and played on the break in the second half, what could we do? [Harkins' challenge] was a good 50-50 tackle that didn't merit a sending-off, maybe a booking at most. We had to compete, but there's not one player who is dirty or over the top. To say I'm disappointed is an understatement, but it worked out OK in the end."
Barrie McKay brought some penetration to Rangers' play as a substitute, with one cross leading to Dean Shiels volleying over. Andy Little found the target with a header, but Malin was equal to the challenge and saved well. "A disappointing day," said McCoist. "But we have got to give Elgin credit."
A trial and error