The 32-year-old Frenchman, who penned a new six-month contract with the Grecians last week to take his stay until the end of the season, has made just six appearances so far this campaign as Ryan Harley, David Noble, James Dunne and Liam Sercombe have all been picked ahead of him.
Cozic told thisisdevon.co.uk: "We have many good players here and they have all done very well. I am happy to play when the manager wants me to play and do a job when it is there to be done."
On signing his new contract, he added: "It is most definitely a happy thing for me to be able to sign another contract. I have always enjoyed my time with Exeter and I want to carry on enjoying it.
"I have a good relationship with the manager and with the other players so it was not a difficult decision for me to extend the contract.
"I have other interests off the pitch, but they don't interfere with the football. When I am playing football, at training or during a match, I will always give more than 100% for the club. I have always done that for Exeter and I will continue to do that."