The Cup holders said on www.fcbarcelona.com that they will also appeal Sergio Busquets' yellow card in the game, which finished 1-1 and sealed a 3-2 aggregate victory to put Barca in the King's Cup final for the fourth successive year.
Busquets is not suspended for the final, while Barca are not appealing against the decision to send off defender Sergi Roberto, who is banned from playing in the final, for receiving two yellow cards.
Referee Jesus Gil Manzano said in a report that he booked Suarez in the 90th minute for "striking his arm against a rival player in a reckless fashion while contesting the ball", while Busquets was carded for "kicking the ball out of play when a free-kick was due to be taken, in a sign of disagreement".
Barcelona said there was an extra ball on the pitch when Busquets booted the other one away.
Suarez expressed disbelief at getting sent off after the game on Tuesday, claiming that Atletico midfielder Koke had exaggerated the impact of the incident in order to get him sent off.
"I'm laughing at that second yellow card, it's not even a foul," the striker told Gol TV after his first red card as a Barcelona player.
"I did absolutely nothing. It was what he (Koke) wanted."
Barca also said defender Javier Mascherano injured his hamstring in the game, making him a doubt for Saturday's trip to Alaves and Tuesday's Champions League last 16 first leg at Paris St Germain.