Ronaldo scored both goals in the 2-0 win at the Bernabeu but was shown a straight red card in the 70th minute after catching defender Patrick Mtiliga with a flailing arm and breaking his nose.
The Spanish football federation (RFEF) said on Tuesday the Portugal forward had been suspended and fined 600 euros.
If Real's attempts to get the ban reversed, reduced or postponed are unsuccessful he will miss Saturday's trip to Deportivo Coruna and the home game against Espanyol the following weekend.
"I wasn't impressed (about the suspension), of course," Ronaldo was quoted as saying by As newspaper on Wednesday.
"I sincerely believe the punishment is excessive," he added. "I am confident in the appeal the club is going to lodge and that the punishment will be reduced."
The RFEF's disciplinary committee decided Ronaldo's actions were not wilful or reckless, which would have meant a longer suspension, but that he had been guilty of dangerous play.
Javier Lopez Farre, Real's legal director, told Cadena Ser radio if the appeal to the RFEF was unsuccessful they would take the case to Spain's Sporting Disciplinary Committee (CEDD), a body overseen by the government sports council (CSD).
"Of course, we would then ask for a postponement (of the ban)," he said. "If the player completes the suspension then it won't help us at all if (the CEDD) rules in our favour."
Messi was awarded a free-kick and Real claimed the incident supported their case for Ronaldo's card to be reversed.
