Raul wants the Spanish giants to be re-established as the best team in Europe.
“The Champions League is the most important competition. It has the best clubs in the continent participating in it,” he said.
“It has traditionally been our competition because we’ve won more European Cups than any other team. We want to recover that.”
Real Madrid lost their first game of the season against Sevilla on Sunday.
“We’ve had a very positive start. Many people have joined the team in this new project and they have to integrate,” he continued.
“We have a new coach (Manuel Pellegrini) with new ideas, so I don’t think you can ask more of us at this stage.
“We can still do much more. We can improve on our performances, but there is nothing better than earning good results at the start of the season.
“We will play well in time. We just need to know each other better and play together more. We have to keep our chances to win titles alive in March, April and May.
“Football has different eras. We’ve gone through a very bad one in recent years. We weren’t in the fight for the title. This new project has brought hope and excitement back.
“This is a great squad, both on a technical and personal level. We want to recover our prestige. We will do our best, especially because the final will take place at the Bernabeu.”