Fabregas managed to gain Conte's favour after only being used sporadically when the Italian arrived at Stamford Bridge at the beginning of last term.
The 30-year-old Spain international says he never doubted what he could offer the Londoners.
"Honestly, no," Fabregas told Marca when asked if thought about parting ways with the Blues.
"I know what I can give the team and if I can play or not so I decided to stay and fight.
"With Antonio, there is no option other than to compete and give 100 per cent in every training session and each match.
"I'm not going to deny it, it was a difficult season.
"I came from playing everything with [Jose] Mourinho and [Guus] Hiddink and then suddenly I was not counted on all of the time.
"Not everyone knows what I went through during those months and there were people who went as far as to say that it was no longer worth it.
"Only my family knows what I have been through."