It is widely accepted that this is a transitional season for Chelsea, but Cech does not see that as a reason to end the term empty-handed.
Gary Cahill joined the squad this week, representing Andre Villas-Boas's fourth major signing as the Portuguese boss continues to rebuild the side.
However, the Blues have never gone two seasons without winning a trophy since Roman Ambramovich bought the club.
"We set a standard in recent years, and that's the way it is at a big club - especially here," said Cech.
"We want, ourselves, to win something. We don't want to go another season without trophies, so our aim is to end this season with silverware.
"We're doing everything in our power to achieve that, alongside the transformation and transition of the team. I think it will be a good year to build on for the future."
Chelsea have been buoyed by news of midfield stalwart Michael Essien's return from injury.