Alexander gifted part-time minnows Elgin a point at Ibrox with an absolute howler late on. The goalkeeper tossed the ball into the back of his own net – and the 10- man visitors held on to draw the match 1-1.
However, McCoist is confident the 34-year-old, who is in talks about sign-ing a new deal, will not let it affect his confidence.
He said: "Neil is a big enough boy to cope with it. He has been in the game long enough to handle situations like this.
"Goalkeepers make mistakes and everybody sees them. Invariably they cost a goal. Other boys make mistakes and get away with it.
"We sat down first thing this morning, looked at it again and had a chat about it. I know it won't be an issue for Neil.
"We didn't play with any tempo, we seemed to be happy running around in front of people, we didn't have any penetra-tion. It was a problem.
"You have to give credit to Elgin for their display, but with the chances we created we should have been out of sight.
"It was very, very frustrating. I said to the boys at half-time that if it stays 1-0 they will get a chance at a free-kick. I told them not to give away a silly free-kick.
"But we did exactly that, we defended it appallingly and gave away a comical goal. We got what we deserved at the end of the day in a game we should have won.
"We will now try to kick on again. The draw against Elgin was the first points we had dropped in 13 league games.
"We are disappointed, but we will try to put the result behind us and get back to winning ways against Berwick."