Rangers were punished by an Scottish Football Association judicial panel last month but had hoped to overturn the decision at Wednesday's appellate tribunal hearing.
But in findings released by the SFA, the club were told they had no grounds for reversing the decision. Duff and Phelps hit back within the hour to register their disappointment at the ruling.
Paul Clark, joint administrator, said: "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."