Rangers' administrators have argued the Scottish FA's decision to uphold a registration embargo is not enforceable under the governing body's rulebook.
The Ibrox side's appeal to overturn the ban, as well as fines of £160,000, was rejected by a tribunal on Wednesday night.
A statement from Duff and Phelps read: "The decision by the appellate tribunal to uphold the sanction, namely the suspension of registration of players for one year, is not competent in the view of the club and its legal advisers.
"Such a sanction was not available to the tribunal and should not have been imposed and it is the intention of the club to challenge the determination.
"The club will consider seeking review of this most disappointing decision and it is a matter of regret that the certainty and finality Rangers sought on this matter has not been achieved.
"Everyone at Rangers is bitterly disappointed and dismayed at this outcome."
The initial disciplinary tribunal imposed the maximum available punishment on Rangers of £100,000, following their failure to pay up to £13m in PAYE, NIC and VAT on employee wages.
Ruling the sanction was insufficient given the level of the offence, the panel exercised a clause in the Scottish FA's articles of association allowing them to impose any additional punishment they saw fit.
As such, the decision to ban the club from signing players aged 18 or over for 12 months was imposed.
Richard Keen QC represented Rangers at the appeals hearing at Hampden, which was heard by Lord Carloway, Craig Graham and Allan Cowan.
Should the club wish to take the matter any further, FIFA's Dispute Resolution Chamber is their next port of call, followed by a potential case to the Court of Arbitration for Sport.
More About Focus on Rangers
- Scottish FA board to consider Rangers 'no links with Craig Whyte' findings
- Rangers talks continue over meeting to remove Malcolm Murray
- Ex-Rangers chief Charles Green agrees to sell shares to hedge fund
- Rangers signings can't play as trialists if league reconstruction approved
- Strachan: Walter Smith the man to get Rangers challenging Celtic again
- Walter Smith new chairman of Rangers as Malcolm Murray stands down
- Rangers inquiry finds 'no evidence' of Craig Whyte link with newco