Mourinho was sacked in December 2015, following a poor run of results at Chelsea while Guus Hiddink was appointed replace him temporarily.
Fabregas said it was the players who had let Mourinho down and that the Portuguese's was too generous to his squad after they won the title by eight points last term.
"I love Jose and consider him my friend... He gave us more holiday because we were champions, he believed in us more, trusted us more, and we let him down," Fabregas told Sky Sports' Monday Night Football.
"That was the main reason why at the end he had to go. And for that, myself and all the team, will feel bad for him."
Italy coach as the next manager and Fabregas believes that the uncompromising attitude to hard work of the incoming manager is exactly what is needed to galvanize the outgoing Premier League champions.
"From what I've heard... he's disciplined, he's a winner and he's a competitor," Fabregas said.
"That's what we need. Someone that will always be on our back to push us and make us work hard, teaching us new things.
"All I know is that he wants to win straight away. No more transition, no more excuses. He wants to win and for that we'll have to be prepared from day one."