The 32-year-old, who trails Diego Lopez in the goalkeeping pecking order at the Bernabeu, made a rare start in a 4-0 romp of Copenhagen in the Champions League on Wednesday.
"It was a long time without playing in the Bernabeu in an official match and getting back to wearing this shirt makes me feel proud," Casillas is quoted as saying by Real's official website.
"It has been a very long time and a lot has happened in that time but I have not tried to hide anything.
"When you've gone so long without playing, lots of things go through your head, but my dream is to keep playing until the mind and body will permit.
"The club has treated me very well and Real Madrid are more important than Casillas.
"What I want is to play football and do so for Real Madrid. Right now, the aim is to keep going."
Casillas lost his place in the side under former Real manager Jose Mourinho midway through last term, with new Los Blancos coach Carlo Ancelotti also preferring Lopez as his first-choice keeper.
Meanwhile, Casillas feels his team responded well in midweek after recently enduring their first La Liga defeat to neighbours Atletico Madrid in 14 years.
"The team should be congratulated because we managed to win, which was not easy," he said.
"The players try to make it better. We have to focus on the present, as we have a team with great quality.
"Real Madrid is the most demanding club and playing in this team and for Spain means that people have opinions of you.
"You have to respect the most critical people and work hard to change their minds so they are with the team so that, together, we can win titles," concluded the World Cup and two-time European Championship winner.