The SPFL League One champions booked their place in the last four with a 2-0 win over Albion Rovers last night as goals from Fraser Aird and Jon Daly clinched a meeting with Jackie McNamara's side next month.
United have complained to the SFA that the game will be played at the Gers' home ground and hit out over the allocation of tickets they will receive.
But with the Arabs looking to fill a sizeable chunk of Ibrox for the clash, McCoist says he doesn't expect his men to gain an advantage by the game taking place in such familiar surroundings.
He said: "Time will tell [how important the Ibrox factor will be]. I don't think United will be fazed by it, that is for sure.
"Their boys play in big stadiums all over, the majority of the boys in their squad have played in big games and semi-finals, some have even won it.
"I don't think the Ibrox factor will faze them at all."
He added: "It would be unfair of me to say that [that the decision was made because clubs thought Rangers might not get there].
"I think obviously the bigger stadiums, like Ibrox and Celtic Park, are the obvious contenders to hold big games.
"I don't think for a minute clubs would have made that decision. I am hopeful that it has been made because it is the perfect stadium to play a big match in and nothing other than that."
Rangers almost saw their cup dreams ended in embarrassing fashion by Rovers first time out but made no mistake second time around.
And McCoist hailed two of his young stars as Calum Gallagher, handed his first start, set up Fraser Aird for the opening goal.
He said: "We were delighted to score first. In the previous game at Ibrox, one of the problems we were faced with was that we lost a goal first and gave the opposition something to hold on to so getting the first goal was a big thing for us.
"Calum has been doing really well, he is a great kid and came on on Saturday and scored his first goal. I thought he did well again for the hour or so against Rovers.
"It was a good goal. Jimmy Sinclair and the boys at Murray Park will be very pleased.
"It was a great cross in and great finish from young Airdy. That was really pleasing. We were delighted to get the second goal to take the pressure off a bit.
"But the first goal, the fact it was two lads coming through from Murray Park added to the pleasure."