Los Blancos suffered an agonising 4-3 defeat to the Bundesliga outfit at the semi-final stage of the tournament, prolonging their wait for an historic 10th European title for at least another season.
Casillas is the sole survivior at the Santiago Bernabeu from the side that last lifted the trophy in 2001, but the Spain skipper insists his side will be "empowered" in their quest for la Decima following the heartbreak of 2012-13.
"We have managed to reach the semi-finals in the last three seasons. We knocked at the door of where Madrid want to be, but this has left a bitter taste because we could have made it to the final," the Spanish international told UEFA.com.
"I'm sure the moment [to win the trophy] will come again so long as we prepare for each match with the motivation and desire we have shown already.
"You only need to see what it does to the fans. On the street people always ask you about it. In fact they demand more and empower you to give your best in this competition and to become kings of Europe again."
Despite the disappointment of failure, Madrid winger Angel Di Maria claimed that losing to a German side in this year's tournament was nothing to be ashamed of due to their strength.
"Bayern had a spectacular campaign in the league, while Dortmund have really come to life – they have some great players," explained the Argentina international.