Los Blancos triumphed in the Copa del Rey last season, but were knocked out of the Champions League at the semi-final stage by Barcelona and also had to settle for second spot in La Liga behind the Catalan club.
However, skipper Casillas believes that Mourinho is keen for the club to win more this time around.
"I still see Mourinho as the same person he was last year, but he is even more ambitious to win trophies now," Casillas is quoted as saying by AS. "That's a good thing in my opinion. His ambition will brush off on the rest of the team. We want to improve on last year's performances.
"We won the Copa del Rey last term and want to retain that trophy and take it one step further in other competitions.
"The coach has said more than once that he's always more successful in his second season, and the players share his ambition."
Madrid face Lyon in the Bernabeu this evening in a Champions League group match.