"My overriding feeling is thanks to the Chelsea fans and the Derby fans and pride at the team".
The lead was short lived as Mount laid on Martyn Waghorn's leveller after 27 minutes before Fabregas' victor.
Lampard, who played with the likes of Cesar Azpilicueta, Willian and David Luiz during his Chelsea days expressed happiness with the performance of his Derby side.
Redknapp was also full of praise for Chelsea loanees Mason Mount and Tomori, particularly with the way the latter responded after scoring a disastrous own goal after five minutes.
But Zola added: "I thought Gary and Christensen in the first half could have done better with the ball". But now they have gone out and they can concentrate on the Championship, which is what is so important now.
Chelsea boss Maurizio Sarri is delighted with the response of his young players this season.
It was January 2015 and he had come on as a 77th-minute substitute for Manchester City, having left Chelsea "through the back door", as he puts it, seven months earlier and controversially joined their biggest Premier League rivals.
Indeed, if veteran striker David Nugent's 89th minute effort had nestled just inside the post instead of bouncing off the woodwork, Lampard would have forced an unwanted extra 30 minutes and perhaps penalties on his beloved Blues.
But Fabregas' goal proved the victor as he took advantage when the ball ricocheted kindly from Chelsea right-back Zappacosta, who was involved in all of their goals.
But him and Cahill looked awkward on the ball and assistant manager Zola admitted that the duo struggled.
"I think we deserved a draw but I'm not upset at all".
A stumbling Waghorn passed up a one-on-one chance to complete a quickfire turnaround and Derby punished themselves through more calamitous defending. It is because we believe in the end of the day is that Mason and Tomori, they grew up as players. We are going to assess him tomorrow.
Lampard said: "The third goal was a foul".
"I've got through and changed mind at the last minute about whether I shift it on to my left foot or square it but in the end I've done neither and tried to get something away last minute", he said.
Chelsea have now won 11 of their past 12 home games against Derby in all competitions, netting 37 goals in those matches (3.1 per game).
Ross Barkley seized his chance to shine in Hazard's absence and scored a goal as well as making two assists in a 4-0 win against Burnley at Turf Moor last weekend.