He told the London Evening Standard: "You have got to show the manager every day that you deserve the jersey.
"That's good for me. It's good to have competition, to be pushed all the way."
He said: 'For me it was very satisfying to make the team and stay in it, but the team is more important than me and it was a hard season for us. We made a good fight for the Champions League but in the end it didn't happen and that is a regret.
'The other big disappointment was the FA Cup Final against Arsenal, although it was a big experience to play in that match.
'Now I really want to help Chelsea win a big trophy.'
Since the end of last season, Chelsea have emphasised their confidence in Cudicini by signing him on a five-year contract.
He said: 'Of course I am very happy with that,' he says. 'It is very important that I know the club have faith in me.
'In return, I want to direct all my ambitions and my energies towards bringing success to the club. I have no realistic international ambitions at the moment. All I am interested in is Chelsea Football Club.'
Cudicini also believes that it is not necessarily a disadvantage that Chelsea have not splashed out in the transfer market.
He said: 'Buying and selling players does not always mean the level goes up. If you cannot sign the talented players, then it is better to stick with what you have, particularly if they know each other very well.'
Stevefurlong@chelsea-mad.co.uk