Fabregas struggled for game time in Conte’s first campaign in charge before breaking his way in, helping Chelsea win the Premier League.
The Spain international has already started 12 league games in 2017-18 – one fewer than he managed all of last season.
But Fabregas said he was concerned about his future at the club during the start of 2016-17.
“I would be lying if said I wasn’t worried. Maybe worried is not the right word but you can imagine,” he said ahead of his side’s Champions League clash against Atletico Madrid.
“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.”
— Chelsea FC (@ChelseaFC) December 4, 2017
Fabregas, 30, is contracted until mid-2019 at Chelsea, the club he joined from Barcelona in June 2014.
The midfielder said he was in no rush to discuss a new deal with his focus on his team.
“I’m very young. I really mean it. Especially how I play, the position, you can go for many more years, I can tell you many cases,” Fabregas said.
“At the end of the year I have a year left but let’s see what happens. I’m where I want to be, enjoying my football, playing week in and week out and I want to enjoy that.
“When the moment comes to talk I’ll be here, ready for it. It’s not the right time, it’s time to focus on Chelsea, keep playing well and deliver points.”