The Stamford Bridge side have never won the competition, and a number of managers have been fired by owner Roman Abramovich in recent years for supposedly not being able to deliver the trophy.
"Show me a team of the stature of Chelsea, Manchester United, Real Madrid or Barcelona who is not obsessed with winning the Champions League," said Cech in The Guardian.
"People always use the word 'obsession' in a negative way, which I'm always amazed by. We are not obsessed in the way that if we don't win it we'll just go and shoot ourselves.
"That's not the case. We are obsessed with the Champions League because this is a great competition to win. In a positive way we try to search for the victory."
Chelsea continue their European campaign on Wednesday when they travel to Valencia.