McCoist - a lifelong Rangers fan who is also the club's record scorer - told the fans he understands how they feel after they were docked 10 points by the Scottish Premier League which effectively handed the title to their Glasgow rivals Celtic.
Rangers, who were chasing a fourth successive title, are now 14 points adrift of Celtic.
"The most important people at this football club have always been the fans and that will always be the case," he told the club's official website ahead of Saturday's home match with Kilmarnock.
"They are suffering at the moment and I am one myself. I have supported the club all my life and I know how they are feeling.
"The one thing that I have to ask them at this time is to be with the club and with the team. The team really need the support of the fans more than ever in this hour.
"They understand that it is not an ideal situation. We have been deducted 10 points and that makes life very, very difficult for us.
"But these are the facts and I would just ask the fans for their continued great support and to please get behind the team."
Rangers, one of the best supported clubs in Britain, are in dispute with Britain's tax authorities and could face a bill of more than £50 million.
Corporate restructuring specialists Duff & Phelps have been appointed by the club to run their affairs, with cost-cutting to try to balance the books now inevitable.
The crisis facing such a big club, champions a world record 54 times, has sent shockwaves through British football where many smaller teams face a precarious existence.
McCoist was confident the Ibrox faithful will not desert him or his players and said he will use the 2008 UEFA Cup final in Manchester, where Rangers narrowly lost to Zenit St. Petersburg, as inspiration to cope with the situation.
"I can still close my eyes and see our fans in that stadium down in Manchester and that will live with me until my dying day. It was incredible support for the team and we have had that over our 140 years," he said.
"I'm biased but I make no apology for that, I believe we have the best fans in the world and I think that will show in the next few weeks."
Rangers and Celtic comprise the "Old Firm" which has dominated Scottish football for more than a century.
The two clubs have no real rivals to challenge them for the title, which either one of them has won every season since Sir Alex Ferguson's Aberdeen triumphed in 1985.
Their dominance and lack of genuine competition is at the heart of the problems of Scottish football and while there have been many suggestions over the years for the two to be admitted to the English League, the idea is unlikely ever to be sanctioned by all the relevant ruling bodies.
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