The Light Blues decided to boycott the game on February 2 in protest at the treatment they received from their former SPL rivals last summer.
McCoist said: "We have come out with a statement saying we don't want to take any tickets. I would hope they (Rangers fans) would respect that."
Dundee United chairman Stephen Thompson was outspoken about the prospect of the troubled Ibrox club being allowed straight back into the top flight.
But the Taysiders have taken the controversial step of selling direct to Gers supporters – and around 200 people have bought briefs for the fifth round tie.
McCoist added: "I'm of the opinion that, rightly or wrongly, we stood up and said we weren't going to take any tickets and that decision should have been, for me, unanimous.
"We should do things together both as a team, as a support. We either all go or none of us go.
"I can understand that the fans will want to go and support the younger lads in a very, very tough away fixture.
"It is difficult at the best of times. They knocked us out twice when we had seasoned professionals and internationalists. So that's how difficult it will be.
"I don't even think we're taking many up in terms of the board and directors, I'm not sure what the set-up is, but we will definitely be there in limited numbers.
"I can totally understand why a fan would want to come.
"But the reason he's not able to support his team is because he has taken the advice of the football club he loves."
McCoist suggested there would be no repeat of the boycott if Rangers are drawn to play an SPL club in the future.
He said: "We'd need to cross that bridge if and when we come to it. But I don't foresee any problem at this moment in time.
"We'd just need to wait and see if and when it happens. Hopefully it will happen as that would have meant we would have won the United game."
Meanwhile, the kick-off times of four Rangers league games, and the date and kick-off time of one league game, have been changed.
The game against East Stirlingshire at Ibrox on Saturday, March 2, will get underway at noon due to it being screened live by ESPN – if Rangers are no longer involved in the Scottish Cup.
The meeting with Elgin City at Borough Briggs on Saturday, March 16, will now kick-off at 12.45pm and will be shown on Sky Sports.
The match with Stilring Albion at Ibrox the following week will be played at noon. The meeting with Montrose at Links Park on Saturday, March 30, will be at noon.
The Glasgow derby game with Queen's Park at Hampden has been moved from Saturday, April 6, to Sunday, April 7, and will now kick off at noon. Those three matches will also be shown by ESPN.