The Third Division leaders were on course for their 12th win in succession after Lewis Macleod's opener.
But the Rangers goalkeeper then block a Stewart Leslie header before fumbling the ball into the back of his own net with just three minutes to go.
The late equaliser 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."
McCoist - who fears defender Ross Perry has suffered a broken nose following a clash of heads - was equally disappointed with his side's efforts in attack though.
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."