Chelsea have not won the league since 2006, when they were under the leadership of Jose Mourinho, and new manager Carlo Ancelotti has made no secret of how important it is that they win some silverware this season.
Eager to add to his medal collection, Cech said: "For the last three years we've had to watch United lifting the trophy and that's frustrating. As a footballer you want to win trophies and you want more when you know how it tastes.
"It is our motivation to bring the trophy back to Stamford Bridge. We have to hope this season will be the lucky one."
Chelsea travel to Aston Villa this weekend following a week-long break for international duty and Cech says the side are looking to prove that their 3-1 loss to Wigan will not be a regular feature to the club's season.
"When you have a good start, even in the games you don't play particularly well in, you manage to win the games and that's a good sign," Cech said.
"After the Wigan game, when we didn't play well and lost, we had a great reaction against Liverpool and now we've got Villa away which is always a difficult game.
"If we can get three points we'll have another advantage."
Cech will return to the side this weekend following a two match suspension. Chelsea will also be boosted by news that Joe Cole is available.