The goalkeeper was jubilant after Sergio Ramos took the Champions League final into extra-time before Real Madrid thrashed Atletico with a 4-1 win.
Atletico Madrid took the lead when the club captain sped off his line uncertainly only to watch Diego Godin's header fly over his head, and Casillas was unable to sprint back in time to keep it from going in.
Godin's goal looked set to decide the game until deep into second-half stoppage-time, when Sergio Ramos equalized to send the all-Madrid clash into extra time.
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Casillas showed his appreciation to Madrid and Spain teammate Ramos with a kiss after the 90 minutes had been played out and eventually lifted the trophy after goals from Gareth Bale, Marcelo and Cristiano Ronaldo wrapped up a 4-1 win.
The Spanish club has waited since 2002 to lay its hands on a 10th European crown and Casillas admits it is a greater achievement than the prospect of defending his global title with Spain this summer.
"La Decima is so important, it's more so than the World Cup," the Spain veteran told reporters after the match. "It's been so long to wait for La Decima, but it's a round number, a perfect number. I want to congratulate those who have come here and thank the fans who have not said anything bad. We suffered. They got a fortunate goal when I made a mistake.
"They had more chances and we kept coming several times. We suffered more than necessary into stoppage time. It seems like a fair result. They defended well, killing time at the end of the 90 minutes, but we did it.
"It’s what we have. Hopefully people will remember La Decima was won in Lisbon. Sometimes we fail, other times we hit the jackpot and I can’t complain."
The European cup is the club's second trophy of the season, after it also lifted the Copa del Rey last month with a 2-1 win over Barcelona.