If I were a Chelsea fan, I wouldn't overly look into the whole Fabregas thing if being honest, not saying he doesn't deserve to start, but it's not as if his absence cost you the 3 points, as it wasn't as if you didn't create the chances to have the game wrapped up, if the case were that you didn't create chances & were the second best team throughout, then I'd be asking the question as to why Conte wasn't starting him.
What I'd be more concerned about is how sloppy & indecisive your back four were, it's not as if they had a lot to deal with, but when they did, it was poor; two shots on target (including a penalty, so just one from open play), two goals. I had similar thoughts in the Liverpool/Burnley game, so I can't wait to see this game next weekend, could be an absolute cracker once both of these back four's get constant waves of attacks flowing at them, could replicate the Arsenal/Liverpool game on the opening Super Sunday.