Smith revealed Lloyds Banking Group were effectively overseeing the club's finances after placing a representative on the board.
The bank denied they were controlling the club while Rangers stressed there was no need to sell players in January despite debts of around £30million.
But worried fans have sought to help improve the club's plight as majority shareholder Sir David Murray seeks a buyer.
Bain said: "It has been a difficult period for fans both in regard to results and speculation about the future of the club.
"However, they have stepped up to the plate in their thousands to voice their support for Rangers.
"We have been inundated with emails, letters and phone calls and the overarching message from the fans is that the interests of Rangers must come first and foremost - a sentiment held dear by the board of directors, Walter Smith and myself.
"I cannot express strongly enough the club's gratitude for this show of support and it reflects the true spirit of Rangers.
"Numerous supporters have expressed a desire to help the club in one way or another. This is appreciated greatly by all of us at Rangers.
"One clear way for fans to assist the club at this stage is to help ensure that our team has the continued benefit of our full support.
"It means so much to the players in both domestic and European fixtures and it would benefit the overall welfare of the club."
Bain added there was no update to the situation regarding a sale.
Rangers are still awaiting a rearranged date for their Clydesdale Bank Premier League clash against Dundee United after Sunday's Tannadice was abandoned due to a waterlogged pitch with the visitors 1-0 ahead.
"We understand fully the frustration of fans who travelled to Dundee yesterday only to see the match abandoned at half-time but these were exceptional circumstances and the management fully supported the referee's decision," Bain told www.rangersfc.co.uk.
"We await the outcome of rescheduling from the Scottish Premier League and Dundee United."