Former Ibrox director Paul Murray and Sale Sharks owner Brian Kennedy made the claim as they withdraw an £11 million offer, after their legal advisers said it was too late for the club to be rescued for the start of next season.
The warning came as controversial former Sheffield United chief executive Charles Green was fronting an English-based consortium bidding for Rangers. It is expected to be given preferred bidder status.
The Blue Knights' departure prompted a war of words with administrators Duff & Phelps as concerns grew that delays were pushing the club to liquidation.
The Blue Knights said it had completed due dilligence and could have "quickly executed" a deal that totalled £11m.
It said it comprised £5.5m up front, plus an extra £3.5m to pay debtors and a further £2m dependent on European success in seasons two and three.
The bid depended on a successful Company Voluntary Arrangement (CVA), the delivery of owner Craig Whyte's 85% majority shareholding and the release of his security over the assets of the club.
Mr Murray and Mr Kennedy told a press conference yesterday their legal advisers felt it was now too late for them to take the crisis-hit club out of administration in time for the start of next season through a successful CVA.
Mr Kennedy said: "The administrators are now saying the quantum of the other party is greater than ours.
"This game could go on for ever and ever and ever until it is too late. Tomorrow morning, it's too late.
"I'd be delighted if Duff & Phelps is able to pull one out of the hat and come up with a fantastic bidder. I fear it may not be able to do that.
"We see the only way forward for the club is to effect a CVA and unfortunately time has run out."
He added: "There is no time left to effect a successful CVA and to exit the club in a healthy capacity from that process. We told Duff & Phelps that on a number of occasions.
"The process has gone on far, far too long for various reasons."
The administrators revealed they had an agreement in principle for Whyte's shares – bought from Sir David Murray for £1 a year ago – on condition Paul Murray was not on the board. The row continued last night as David Hinchcliffe, legal adviser of the Blue Knights, wrote in an email to David Whitehouse, the joint administrator of Duff & Phelps, saying: "If you want to talk to find a way to save this great club Brian has said his phone will be on this evening. Otherwise I fear it will be too late David."
Duff & Phelps said it was told there was "no agreement" within the Blue Knights consortium in relation to the funding of their bid.
Mr Whitehouse said: "Time and again he and others have been afforded the opportunity to become the best bid in play and it has not happened.
"We have a statutory duty to accept the best bid that is deliverable."
The Blue Knights was front runner for control at Ibrox several weeks ago, but potential partners Ticketus would not pay the £500,000 exclusivity fee and an agreement on funding a takeover collapsed.
After joining Mr Kennedy, and without Ticketus, the consortium was then beaten to preferred bidder status by US trucks tycoon Bill Miller, who subsequently withdrew.
Mr Kennedy revealed he tried to persuade Mr Miller to drop his plan to form a "newco" three weeks before being made preferred bidder and, if he did not want to do a CVA, to join the Blue Knights to save Rangers, providing "£27m of quantum".
"They weren't interested, they wanted to go forward on a newco basis. I knew it didn't work. They found out it didn't work," he said.
While announcing their exit, Mr Kennedy and Mr Murray then proceeded to detail their plans for the club, which included a "phenomenal team" of former managers Walter Smith and Graeme Souness working part-time on a "football board" along with Ally McCoist as team manager.
The pair criticised the way Duff & Phelps had handled the bidding process and their bid during a hastily convened press conference yesterday.
Mr Kennedy said: "By virtue of the fact Duff & Phelps has chosen not to go with us as preferred bidder, it better have someone good to come along to Rangers, some good credible consortium, fully funded who does not fall away next week and the result being the liquidation of Rangers Football Club.
"I don't care if ours was not the largest bid, when you have an institution like this that's at death's door what's important is not just quantum ... it's deliverability.
"We can't afford to make another mistake.
"Anyone with a brain in their head can see this is a credible plan that's fully funded by credible people with the right motive.
"I spent three hours at Craig Whyte's castle talking about Rangers with Craig Whyte. He's had a lot of bad press and wants Rangers to survive. He agreed to give me his shares."
Mr Kennedy had selected former Scottish Rugby Union chief executive Gordon McKie to run Rangers.
"We have had people in there doing due diligence. We aren't going to find anything that is going to surprise us. We could quickly execute this deal.
"This is about Rangers Football Club surviving. We would be delighted if Duff & Phelps pull one out the hat and come up with a fantastic bidder that was going to safeguard the club. We fear they may not be able to do that."
Mr Murray said: "People are trying to help the club. I find it perplexing that Duff & Phelps go about questioning why we are doing things, misrepresenting us."
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