Light Blues supporters were unimpressed with the 2-1 win over part-time Brechin City on Saturday. It was the second time in eight days the Gers have struggled to beat SPFL League One rivals at home.
The fans left inside Ibrox at the final whistle let the players know how unhappy they were in no uncertain terms.
But McCoist is confident his charges will handle criticism and said it would help them keep winning. He said: "I can understand the fans' frustration. If anything, it keeps us on our toes.
"We could sense the nervousness when there was only one goal in it and there was still an opportunity for the opposition to equalise.
"But it has been here for 100 years and it will be here for another 100 years. It is just something the players are going to have to handle."
McCoist added: "I used to get a wee bit of stick myself when I played. You just have to keep taking the ball and learn how to handle it.
"Ibrox is a great place to play - but it can be a difficult place to play. You have to stand up and I have no doubt the boys we have here will."
Meanwhile, McCoist has promised to speak to Rangers centre-half Bilel Mohsni this week after his pointless dismissal.
Mohsni was given a second yellow by referee Stevie O'Reilly in the second half after kicking the ball at Brechin's Allan Walker.
McCoist said: "I was extremely disappointed. Bilel gives the referee the opportunity to give him a second yellow card and the referee took that opportunity.
"I didn't have a problem with it from the referee's point of view. But from our point of view I am extremely disappointed.
"I plan to speak to him about it. He should know much better. You get taught not to do things like that when you are at school. It was a needless second yellow card."