Suarez received his marching orders in stoppage time as two-time defending champions Barca advanced to a third successive final 3-2 on aggregate following Tuesday's 1-1 second-leg draw at home to Atletico Madrid.
The Uruguay international opened the scoring prior to half-time, before he was shown a second yellow card after an aerial challenge with Koke in the closing stages, having also seen team-mate Sergi Roberto sent off.
Luis Enrique, however, does not fancy Barcelona's chances of having Suarez available for the decider on May 27.
"I'm in agreement with appealing, but if you look at the past you will see what good appeals have been for us," he said.
"[The final is] not until May, there's a long time to think about that [who would replace Suarez].
"It frustrates me that players on my team miss finals, but at the end of the day it's something which happens in football. The referee felt that both Suarez and Roberto deserved two yellow cards.
"I was about to take Roberto off because of the booking he had. He's made three challenges and he's been given two cautions. We felt he could maybe get a second, but we didn't react quick enough."
Barca, who ended the match with nine men, were made to suffer after substitute Kevin Gameiro levelled proceedings on the night with seven minutes remaining.
Atletico's Antoine Griezmann also had a goal incorrectly disallowed for offside in the second half.
"In the 90 minutes we did not deserve this result, but we deserve to play the final of Copa del Rey because of the merits we have made in the competition," Luis Enrique added.