The Irn-Bru Third Division leaders looked set to hold on for their 12th win in a row after Lewis Macleod claimed an early opener, but an horrendous mistake saw the Light Blues number one appear to block a Stewart Leslie header before fumbling the ball into the back of his own net with just three minutes to go.
The late leveller prevented Rangers from extending their advantage at the summit to 19 points and also cost them their 100% league record at Ibrox this season.
McCoist said: "I haven't spoken to him yet but obviously I will do. I've seen the goal a good few times. He's big enough to recover from it but he knows he made a mistake.
"We will look at it again on Monday. But he's been in the game long enough to handle situations like that.
"Goalkeepers make mistakes and everybody sees them and invariably they cost a goal. Other boys make mistakes and can get away with them. Neil is a big enough boy to handle it."
Rangers netted 14 goals against Elgin in the previous three meetings between the clubs this season, but McCoist - who fears defender Ross Perry has suffered a broken nose following a clash of heads - admits his side simply were not clinical enough this time.
He said: "I said to the players that we mustn't give away silly free-kicks and we gave away a silly free-kick. We defended it appallingly and it was a comical goal to lose.
"There is an argument that we got what we deserved, to be quite honest with you, in a game that we should have won and been very comfortable in. With the chances we created, we should have been out of sight. It was a disappointing day."
Rangers' cause should have been boosted by the dismissal of Paul Harkins for a challenge on Ian Black shortly before half-time. Elgin boss Ross Jack felt referee John Beaton called the sending-off wrong, and said: "I thought it was a good 50-50 tackle. I didn't think it merited a sending-off, probably a booking at most."