Ibrox chief executive Charles Green confirmed after the fifth round draw was made that the club would not be taking their allocation for what will be the first match away to Clydesdale Bank Premier League opposition since Rangers were relaunched as a new company and denied entry to the SPL.
McCoist said: "It goes without saying that we are enjoying arguably our greatest support in terms of numbers and backing in many years so it's not an ideal situation that we won't have any Rangers fans in the stadium. But the club have taken this stance and it's one that I fully support as well.
"There are pros and cons in all the arguments and I can see all sides of the arguments. I've spoken to a couple of the heads of our supporters groups for the opinion of their members and they have told me overwhelmingly that the vast majority - nearly unanimous - didn't want to take tickets for the game.
"I value their opinion very highly and I respect their opinion. We all want to move on but, at the same time, I can understand the stance taken by the supporters. I back them 100%."
A number of top-flight clubs took into account the views of their own supporters when they voted to reject newco Rangers' application for entry to the SPL in the summer.
McCoist added: "When we were voted out of the league, a lot of the chairmen and club representatives told us that they were listening to their fans, which is totally understandable and acceptable.
"With this stance, we've decided to do the same. I would also say we should tread carefully down that road because it's not to say that the fans are going to be 100% right all the time. But I certainly believe they should have a voice and it should be listened to and appreciated."
Some Rangers fans believe United chairman Stephen Thompson was an influential figure in their SPL bid being rejected, before the club was voted into the Irn-Bru Third Division. Asked if fans would favour a similar boycott of future away fixtures against other SPL opposition, McCoist said: "I genuinely don't know.
"I can't answer that question because I don't know what the opinions of the fans are regarding other SPL clubs. What I do know is that they feel quite vociferous and vocal in their support of not taking an allocation at all for this particular game."