Real were disqualified from the event after Denis Cheryshev played in the 3-1 first-leg win over Cadiz on December 2 - this despite his being suspended having accrued three yellow cards with Villarreal last season.
The La Liga giants later lodged appeals with the Royal Spanish Football Federation and the Court of Arbitration for Sport (CAS) but without success.
Los Blancos released a statement, which read: "The club respects the decision of the tribunal which means that the return game cannot be played as scheduled.
"Real Madrid announces that it will proceed immediately with refunds for tickets purchased for said game."
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