The Portuguese left the club in December with the Blues struggling at the wrong end of the Barclays Premier League after losing nine out of 16 games.
The 2015 champions are now 10th - 16 points outside the Champions League places - and Fabregas said he and his Chelsea team-mates "let him down."
"I have huge respect for him - we still keep in touch right now," the former Arsenal and Barcelona player said on Sky Sports' Monday Night Football
"The biggest problem was he trusted us too much, gave us more holiday because we were champions and we let him down
"That was the main reason he had to go - and for that myself and the team feel bad for it."
Fabregas, who spent eight years at Arsenal, also said he wanted Leicester to win the title
Asked, ahead of Tottenham's meeting with Stoke, if he felt there would be another twist in the title race, he said: "Hopefully not, I don't want Spurs to win it to be honest
"For what they've done through the season I'd love Leicester to win the Premier League."
Leicester travel to Chelsea in their final game of the season on May 15
Source : PA
Source: PA