The Russian winger picked up three yellow cards in the competition last season while on loan at Villarreal - the third in the semi-final defeat to Barcelona - and was supposed to be suspended for the first game of this season’s Copa.
However, Madrid did not realise and Rafael Benitez, taking advantage of his squad, played him from the start against the third division side.
Cheryshev opened the scoring, but was taken off 45 second into the second half as word spread that he was not eligible to play.
Cadiz confirmed on Wednesday they had made a complaint to the Spanish Football Federation (RFEF) regarding Cheryshev’s involvement.
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Madrid are now likely to appeal the decision and fight for their right to remain in the Copa del Rey, as Perez suggested they would do during a press conference on Thursday evening.
"The penalty Cheryshev was given while playing for Villarreal is ineffective in our view, no one had mentioned the sanction to the player’” the Madrid president said.
"As Article 41 of the RFEF's disciplinary code states, the punishment is not effective unless it notifies those to be punished.
"Real Madrid did not know of its existence, no one reported it - neither the player nor Villarreal nor the RFEF."
The club’s first move will be to take it to the Appeals Committee, with the option to then take it to the Court of Arbitration for Sport if they are knocked back.