Iker Casillas believes Real Madrid must aim to become champions of Spain and Europe once more after being forced to settle for the Copa del Rey last season.
Madrid enjoyed domestic cup success over Barcelona in April, but they finished four points behind their arch-rivals in the league and were helpless to prevent Barca clinching the Champions League after losing their semi-final meeting.
Madrid have already shown signs of intent by further investing in the squad this summer and, with Jose Mourinho having said that his teams invariably improve after his first year in charge, club captain Casillas feels they should be aiming to re-establish themselves as the finest team in Europe.
"Mourinho has come up with a competitive and more aggressive side," he told ESPN. "He has turned us into a more mature team.
"We have to wait for such a young team to mature, but its first tooth already came out when it won the Copa del Rey. It was a title I had never won before and that proved elusive for Real Madrid. We hadn't won it in 18 years and it meant a lot to us to do so against Barcelona, but we can't settle for just that.
"Real Madrid must always do more. We hope to win much more next year because we are ambitious. Our objectives must be greater next season. I want to win every possible title. I've won two European Cups and I would like a third. I've also got four league titles and would like a fifth. Every new year must be a new challenge."
Cristiano Ronaldo remains central to Madrid's hopes of breaking Barca's recent run of success, but there had been talk of a dressing-room feud when Casillas' girlfriend, Sara Carbonero, described the Portuguese as "selfish and individualistic" in September last year.
On his relationship with Ronaldo, Casillas said: "He's a friend and a team-mate, a team-mate and a friend - but he's also an enemy, because we argue a lot."
He added: "One doesn't net 40 strikes in one season in the league by chance. He's done this more than once, so he must be very good."