The Gers declined to take up a ticket allocation for the fifth-round tie, but after United put briefs on sale there will be a few hundred Light Blues fans in attendance.
The vast majority of the Ibrox support has backed the boycott but McCoist will not condemn those who are heading to Tayside.
The Rangers manager said: "It does not really suit us long term not having any support.
"We have supporters who travel all over the globe, never mind the country. As manager it suits me having supporters who are backing the team. I hope it is a one-off.
"I just think that the club have taken the stance about not taking tickets; that was the club's opinion.
"We don't have a final say on who buys tickets. We totally appreciate that. The most important thing obviously is that everyone behaves themselves and we can enjoy a game of football.
"I am certainly not going to be critical of our fans at any time this season. They have been the real story of our club in the last year.
"They will not be getting any criticism from me, because they have been nothing but fantastic for us."
Tensions between United and Rangers have hit new highs over a series of issues in recent months, leading to fans urging chief executive Charles Green to turn down any ticket allocation for today's clash.
It leaves McCoist and his players in unfamiliar territory as they look to claim an SPL scalp this afternoon and the Gers boss is keen to dampen the flames.
He said: "I think it's time to take a bit of heat out of the situation.
"I know we all have jobs to do; yours (the media) is to build the game up and sell tickets and make it a spectacle. I am fully appreciative of that.
"I just think maybe a wee bit of the build-up has gone a wee bit over the top.
"The factors are that we are not taking any support; we have asked not to take any tickets and we as a club want to be seen to be making a statement, that is all we are doing.
"It is going to be a game between two teams who in years gone by have always had a healthy respect for each other.
"We have had good games with each other. Today will be the same."