The Spain international cut a frustrated figure at times during the Blues' title-winning campaign, starting just 13 Premier League games in total.
Fabregas broke into the first-team fold in the latter stages of the season, however, and has been used far more often so far this time around with 12 starts to his name already.
After earning praise from Conte, the 30-year-old says that he is delighted to have proved his manager wrong.
"I would be lying if said I wasn't worried. Maybe worried is not the right word but you can imagine," he told reporters. "I wasn't playing, not really part of his initial plans and at that point you can do two things.
"You can just give up and accept you're not part of the team or the club in the future or what I did, put your head down, be humble, work hard, train hard every day, show him that he's wrong and that he can can trust me and play in this team.
"Every time I had an opportunity I gave my all, I delivered and from then on we started to create a relationship. Now I can say our relationship is fantastic... I understand his philosophy and must say I am very proud of this, also very happy I am where I want to be and that's all down to belief and trust and hard work."
Fabregas, in line to feature against Atletico Madrid this evening, has played a direct part in six goals in all competitions this season.