Carlo Ancelotti's men face fellow La Liga giants Barcelona in the final at Valencia's Estadio de Mestalla.
The Copa del Rey decider will be Real's third in the past four years, and they are aiming for their second win.
Casillas said his team felt they would win the trophy, with their last success also coming at the Mestalla in 2011.
"Winning is the idea we have, not just me," Casillas told a news conference.
"The team has played a good Copa Del Rey. It won't be easy, it will be an exciting match with great players and we need to believe in our chances and our way of playing.
"We think we are going to do it."
Real face a Barca side who have suffered consecutive 1-0 defeats, the first against Atletico Madrid in the UEFA Champions League and the second at Granada on Saturday.
Gerardo Martino is under pressure with Barca sitting third in the league but Casillas said the Catalans' recent form meant nothing.
"Personally I'm not thinking about Barcelona's last week at all, regarding their defeats in the Champions League and La Liga," Casillas said.
"It's different for the two teams, anything can happen in a final. Now they have two competitions to play for. One will be difficult for them to win and the other is this final.
"We need to forget about the past and concentrate on this final. The team is prepared."
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