Beckham was sent off three minutes from time by referee Arturo Dauden Ibanez after receiving two yellow cards in quick succession, the first for dissent and the second for applauding the decision "in a sarcastic manner".
Real say they will present video evidence and photographs to the Spanish Football Federation's Appeals Committee to show that Beckham's clapping was "neither scornful nor sarcastic."
The club said that Beckham, who has been one of the team's most influential players this season, would travel with the rest of the team to La Coruna on Tuesday in the hope that the sending off would be overturned.
Beckham became the first England player to be sent off twice when he was dismissed in a World Cup qualifier against Austria. He has been sent off three times since joining Real in 2003 and once while at his previous club Manchester United.
Real's Danish midfielder Thomas Gravesen was given a straight red card six minutes before Beckham's dismissal for a reckless challenge on Valencia winger Vicente, but the club are not launching an appeal against that decision.
