"Good question. No, it's not that", Zola said of Lampard's influence in allowing the young duo to play.
But Zola, who conducted Chelsea's pre-match press conference in Maurizio Sarri's stead, denied that Mount and Tomori are just playing to help out an old friend of the club.
Incredibly, the links to Chelsea don't quite end there; the unfortunate goalscorer was one of the club's players out on loan with Lampard's club, Fikayo Tomori.
A near identical own goal - another Zappacosta cross, this time sliced into his own net by Richard Keogh - restored Chelsea's advantage after 21 minutes.
Meanwhile Derby will be boosted by the availability of Fikayo Tomori and Mason Mount for selection, but the latter could still miss out having picked up a minor foot injury against Middlesbrough at the weekend.
Martyn Waghorn drew the visitors level for a second time before Cesc Fabregas struck what proved to be the victor in the 41st-minute.
Ten-man Arsenal were made to sweat by League One Blackpool before eventually emerging 2-1 winners, with goals from Stefan Lichtsteiner and Emile Smith-Rowe.
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England boss Gareth Southgate called Mount into his squad during the recent global break and would have been pleased to witness the 19-year-old feature - and impress.
Lampard took it all in his stride, of course, transitioning effortlessly from clapping the songs directed at him to vigorously applauding his Derby players as they hassled and harried Chelsea into defensive mistakes. It's a terrible own-goal by Tomori who nets for his parent club! Thereafter he performed well. Huddlestone carves open the defence with a lovely ball through to Marriott, who still has plenty to do.
The Rams might have led had Waghorn shown the same composure.
5' - OWN-GOAL! Chelsea 1-0 Derby: Well, would you believe it?
DF Andreas Christensen, 6 - Unsettled by the speed and ferocity of Derby's pressing, he played his way into trouble a few times in a manic first half.
Derby responded once more.
Lampard shook his head in apparent disbelief at the cup tie unfolding before him. The visitors were adamant Zappacosta had fouled Scott Malone in the build-up to the hosts' third, which was eventually dispatched crisply by Fàbregas to fly in off Carson's left hand as the goalkeeper slumped to his right. Managed to stabilise himself in the second, but this isn't the display that will persuade Sarri to pick him over David Luiz, who eventually replaced him. His shot was palmed on to the roof of the net by Caballero. Oh so, so close for Derby!