The William Hill Scottish Cup tie is set to be played in controversial and unusual circumstances after Rangers opted against taking a ticket allocation for the visit to Tannadice.
The club took the decision after fans groups called for a boycott of what will be the first away match against Clydesdale Bank Premier League opposition since the Light Blues were denied entry to the top flight after being consigned to liquidation in the summer.
Around 10,000 home fans are expected to watch Jackie McNamara's debut as United boss, with only a few hundred away fans expected on Tayside.
McCoist, who hopes the situation is a one-off, said: "There has been a lot of stuff written and a lot of stuff said.
"I think now is the time to actually take the sting out of the whole situation to be honest.
"Jackie is a great lad. I wished him all the best in his job and we'll shake hands before the game.
"All it is, is a cup tie that both teams want to win.
"It's going to be a little bit different because the club have taken the stance not to take any tickets for the game.
"That stance has been made and hopefully it's just a one-off and we can move on.
"People are probably reading a lot more into it and wanting to build a lot more out of it than they should.
"It's a cup game that's important to both clubs and both clubs want to win. It's no more than that.
"I do appreciate there will be an edge to the game but we all have a duty and a responsibility to do our best for our clubs and, indeed, behave ourselves.
"That will hopefully be the case."
McCoist has praised fans on many occasions this season for the impressive backing they have shown to Rangers in the Irn-Bru Third Division.
He admits a lack of support against United will make the task tougher, but believes his side can still triumph in the fifth-round tie.
He said: "It's not an ideal situation, of course it's not.
"We would rather take what is a tremendous away support.
"If they followed us to Elgin, Berwick, Peterhead and Forres, I think there is every chance they would have followed us to Dundee as well.
"But circumstances have dictated that we haven't taken a ticket allocation.
"It's not ideal and it will make it more difficult.
"That said, I've played in away games myself where we haven't taken any support which has worked out reasonably well for us.
"I'm keeping my fingers crossed that will be the case tomorrow."
McCoist refused to be critical of Rangers fans who do make the trip to Tannadice.
He added: "We've taken a stance on it and we've already made our views clear on it, that we didn't take any tickets.
"It was all or nothing for me, that's my opinion.
"But we've got such a great support and I can understand that they want to travel all over the world to watch us, and they're proud of the fact that they don't miss any games.
"So I can understand the fans' disappointment and I can understand some fans wanting to go.
"I would imagine some fans will be there and I can totally accept that."
On the match itself, McCoist said: "I'm not attempting to play mind games.
"Dundee United will be favourites, they must be favourites.
"I think the bookies would tell you that and it's not often the bookies get it wrong.
"The best way to put it is, at the start of the season - outside Celtic - Dundee United would have been many people's favourites to win the cup.
"I understand Jackie's views - he's not going to treat us lightly and I didn't think for a minute that he would.
"But Dundee United will start the game as firm favourites."
A transfer embargo meant McCoist was unable to make use of the January transfer window, but is continuing his search for players he can recruit on pre-contract agreements before registering them as free agents in September.
He said: "We've certainly had positives in terms of one or two players who we would like to come, who are out of contract and we can register in September."
Rangers striker Francisco Sandaza is rated doubtful for tomorrow's fifth round tie.
The Spaniard is struggling with a hamstring problem, while skipper Lee McCulloch has failed to recover from an ankle injury in time.
Lewis Macleod also misses the clash at Tannadice after being ruled out for seven weeks with knee ligament damage sustained against Montrose last weekend.
Meanwhile, Jackie McNamara has a full squad to choose from in his first game as Dundee United manager.
United kept their squad intact on transfer deadline day despite reported interest in forward Johnny Russell.
Czech midfielder Rudi Skacel's short-term contract expired on Wednesday.