The club announced losses for the seven months to December 31 of £3.7million, as reported in late editions of yesterday's Evening Times.
It is an improvement of 50% on the same period 12 months earlier, but Neil Patey, a partner at Ernst and Young, said the figures are not improving quickly enough.
He believes boss Ally McCoist will not be able to spend the sums needed to take on Neil Lennon's Celtic, if they win promotion to the top-flight at the end of next season.
Mr Patey said: "Unless they get an external equity injection, the fact is Rangers will not be able to compete financially with Celtic until they get back into the Champions League.
"How much will it take? It's difficult to say but Celtic have been pulling in £10m to £15m from Europe for the last couple of years.
"So that gives you an idea kind of money Rangers are missing out on.
"It will require tens of millions, for sure."
The financial results arrive after criticism of the board by fans groups and former director Dave King.
Businessman Dave King this week revealed he could plough up to £50m into the Gers to help them get in shape on and off the field.
Mr Patey added: "The club have improved revenue and cut costs so they are heading in the right direction, but there is some way to go before they achieve break-even.
"Rangers are now heading up the leagues which will bring in extra revenue for things like increased season-ticket fees, prize money and possibly European football once they are in the top flight.
"But they are not at the stage yet where they can stop relying on external injections of cash.
"There needs to be further cost-cutting and Graham Wallace's 120-day review should deal with that."
HE continued: "However, for Rangers to get to break-even before they return to the Premiership would be a big challenge."
Rangers chairman David Somers has said "uncertainty" over season ticket income could cast doubt on the club's ability to continue.
But the club had just £3.5m cash on December 31, despite bringing in £22m in an initial public offering (IPO) share issue just over a year earlier.
The main Rangers supporters' groups recently raised the possibility of drip-feeding season ticket money to the club via a trust fund amid distrust over the board.
And the club, who recently arranged loans totalling £1.5m from two shareholders, admits that casts a shadow over the club's immediate future.
In the interim report, Somers said: "This possibility results in the existence of a material uncertainty which may cast doubt about Rangers' ability to continue as a going concern and therefore that the company may be unable to realise its assets and discharge its liabilities in the normal course of business.
"The directors have concluded that there is a reasonable expectation that the company has adequate resources to continue for the foreseeable future."