Derby assistant Jody Morris, victor of seven trophies in two seasons in charge of the Blues' under-18 and under-19 sides before leaving to team up with Lampard, also got his moment of appreciation at the final whistle.
His Derby side booked their fourth-round berth with a penalty shoot-out win over Manchester United at Old Trafford, the Rams have drawn against Chelsea in the subsequent draw.
GK Willy Caballero, 6 - Could do nothing about either of Derby's goals, but his distribution was poor and nothing about him inspired confidence in his defenders.
If Derby do end up knocking out Chelsea, there would surely be different questions being asked of the club, as is the work of the fans and pundits, so it is best to leave their business alone.
'It looks like they are in good hands and the coaching they are getting is excellent.
He may never be much more than an understudy to Cesar Azpilicueta, but right-back Zappacosta at least left an imprint of his attacking ability in Sarri's mind, the Italian having been involved in all three Chelsea goals.
A quieter second half eventually livened up, with substitute Nugent turning the last of three Derby openings into the base of the far post, forcing Lampard to settle for the consolation of receiving the adulation of the supporters, who consistently sung his name.More news: Trump's North Korea Envoy Strikes Out in Meeting His Counterpart
Undaunted, Lampard's side levelled shortly before the half-hour through Martyn Waghorn before Cesc Fabregas restored order for the Premier League high-flyers.
Ruben Loftus-Cheek could start as a result and Mateo Kovacic could play to try to play himself into form. In a statement released last week, Chelsea admitted they thought the experience from the match would be beneficial to both Mount and Tomori's development at Derby.
Chelsea fans welcomed Frank Lampard back to Stamford Bridge.
Zola sees no reason why Mount and Tomori could not celebrate a Derby goal or victory.
DF David Luiz, 6 - Brought on for Christensen to give Chelsea greater defensive solidity, he broadly did his job as Derby pushed in vain for an equaliser in the final 20 minutes. His forward runs were just as risky to Chelsea as to the opponents; both visiting goals came from the space vacated on his flank.
"The difference between the sides was they scored three. actually we scored four didn't we?"
With rotation likely, Loftus-Cheek will be one of the favourites to start for Chelsea and could yet again find the net. "That's why he scored so many goals".