The Scottish champions' only hope of silverware this season now depends on resurrecting their SPL title bid after falling a point behind leaders Celtic, who have a game in hand.
But as far as McCoist is concerned, the wait for a verdict in a tax tribunal with Her Majesty's Revenue and Customs (HMRC) that could land the club with a bill of £49million remains the biggest problem.
Asked if the club is now in crisis, McCoist said: "I think the crisis point comes with the tax case more than anything.
"That's the biggest problem that the club faces. I don't think there is any doubt about that.
"What we all need is clarification on what's happening so that we can move forward. The uncertainty regarding this tax issue is the biggest problem that we have.
"You could use the word 'crisis' in terms of the tax case, but we need to know one way or another where it stands and what we face so we can deal with it and move forward."
McCoist was unable to replace top goalscorer Nikica Jelavic ahead of the transfer deadline, but could yet bolster his squad with free agents and expects to have the backing of owner Craig Whyte.
He said: "I think if I went to Craig with a player that we could maybe bring in he would certainly have a look at it. We've got two or three targets.
"I haven't gone as far as the finances but I know two or three players that would be appealing to us.
"But I will not bring anybody in who I don't think can go into the team or better the squad. I don't think there is any point in that at all."
Rangers' need for new players was highlighted when they ended Sunday's fifth-round tie with a front pairing of Salim Kerkar - who has never started a game - and Andrew Little, whose injury problems meant he had not featured for the club since October 2010.
McCoist added: "We have injury problems in that department. Kyle Lafferty and Steven Naismith can both play there.
"We're going with two not really recognised strikers for the last 15 or 20 minutes but that's where we are.
"I don't have any complaints about how the two lads went about it, I just felt we lacked a bit of quality to open up United today and that was a disappointing thing."
Meanwhile, McCoist denied reports that Rangers were ready to sell Kyle Lafferty - who is sidelined with a torn hamstring - to an English club for £1.75million.
He said: "To my knowledge that's absolute nonsense. We have been trying to re-sign Lafferty and offer him a new deal.
"That's my views on it and that's crystal clear. I know nothing about trying to sell Lafferty and I certainly don't know of any bids that came in. I told the player that this morning as well."
Asked if a deal could have been struck without his knowledge, McCoist replied: "I wouldn't have thought so, no."
First-half goals from Gavin Gunning and Johnny Russell secured a comfortable victory for United, but McCoist is confident his players will bounce back.
He said: "The players are fine. They just get the sleeves rolled up and get on with it. That's the only way we go.
"The players are disappointed but, come Monday morning, we'll get back into training and go ahead.
"This club has had problems in the past but it's determination and grit and a lot of qualities that we have in that dressing room that will see us through this."
United boss Peter Houston backed McCoist to transform Rangers' fortunes but insists his side deserved credit for the win.
He said: "We weren't concerned with what's going on at Rangers. Rangers have got a good squad of players.
"Coisty will turn it around. He's a fantastic manager and I think he's going to be a great manager long term for Rangers.
"I put this result down to what we did, rather than what Rangers didn't do."
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