The Ibrox outfit have announced a loss of £3.7million in the seven months up to the end of 2013 - an improvement of 50 per cent on the same period 12 months earlier.
But the interim results also showed that, by December 31, the club had just £3.5million left of the £22million raised when it was floated on the stock market 13 months earlier.
And the accounts stated that, within that cash balance, nearly £1.7million relating to Rangers Retail Limited "is not immediately available as working capital to the group as a whole".
Since the period, the League One champions have been forced to take out loans totalling £1.5million from two shareholders.
And the Union of Fans, representing the main Rangers supporter groups, insists that runs counter to Wallace's AGM claim that there was "sufficient cash in the business to fund the ongoing needs of the club in the near term".
In a statement, the coalition group said: "It appears from both these interim results and the recent loan of £1.5million that this statement at the AGM may have been somewhat misleading.
"It is unclear exactly how it could have been stated by the board at that time, with any confidence, that there was sufficient cash even for the short term and we would like Mr Wallace and (chairman David) Somers to explain this as a matter of urgency."
Rangers declined to comment on suggestions Wallace had misled supporters, but the Union of Fans also took issue with Somers' comments about plans for a season-ticket trust.
The fans, angered by the board's management, have collected pledges from more than 6,500 fans who vow to pay ticket fees into a collective account which would only be handed over to the board once they have given assurances about the club's future.
Plans for the money to be drip-fed to the ruling regime have been dropped but the Union of Fans will demand security on Ibrox and Murray Park before releasing the lump sum.
Somers claimed those plans mean there is "material uncertainty" over the club's ability to continue as a going concern - a position backed by auditors Deloitte, who reported a "significant" risk.
In the interim report, Somers attacked "ill-informed opinion" surrounding the debate before criticising the ticket trust plans, saying: "If this were to happen then there would be a negative impact on short-term cash balances and it is possible that the club may need to seek alternative additional short term financing. This clearly would not be in the best interests of Rangers."
But the fans group responded: "It would be foolhardy for fans to once again commit their money without any kind of transparency or security. The fans have shown outstanding loyalty in the past two years but we have seen that loyalty thrown back in our faces as money has been squandered."
The interim report follows months of uncertainty about Rangers' financial health.
The document assumes Rangers will "modestly" increase season-ticket numbers, which stood at 36,000 in League One, next season and beyond.
The improved financial results are largely down to increased retail sales, with the club's Sports Direct partnership worth £4.8million in the seven months, up from £900,000.
Revenue was up 38 per cent to £13.2million but operating expenses also increased slightly to £16.8million.
Staff costs were down £800,000 to £7.5million, with £500,000 spent on severance payments.
Somers and Wallace were appointed towards the end of the period. The chief executive is conducting a 120-day review of the business and claims to be making "excellent progress" towards a new vision for the club.
But Somers tried to detail where the £22million raised by shareholders had gone, explaining: "The majority of the IPO money had been spent by June 2013 on IPO related fees and commissions, severance payments, the purchases of the Albion car park and Edmiston House and to fund ongoing operating losses.
"The club incurred a further £7.7m of cash expenditure in the six months to 31 December 2013, funding additional fixed asset purchases and operating losses. In total the club has spent over £4m on fixed assets since the IPO that are not yet generating incremental revenue."
Somers admitted operating costs had been unsustainable.
"For example, in the period under review, nine players were signed at a time when the club already had the second highest wage bill in Scottish football whilst playing in the third tier," he added.
Meanwhile, the club detailed possible legal action by Craig Whyte in the "contingent liabilities" of the report, but stated they had not had any correspondence from the former Rangers owner since May.
Whyte had claimed he was deprived of a legitimate interest in the new company which rose from the ashes of the club he pushed towards liquidation, but that has been rejected by Rangers.