The size of the challenge to beat Chelsea was huge for Derby, with no win here since 1983 and no clean sheet since Peter Shilton's blank in 1987.
A pair of own goals in the opening 21 minutes made their task even tougher in London and a close-range Cesc Fabregas finish shortly before half-time provided the telling blow.
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.
"This wasn't the game for Mason to run it like he does", Lampard said after the game.
The match sees Chelsea's all-time top goalscorer Lampard return to Stamford Bridge for the first time as a manager, aided by former Blues midfielder Jody Morris. They also eliminated Manchester United in the third round, triumphing 8-7 on penalties at Old Trafford.
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That was the view of Chelsea assistant manager Gianfranco Zola, who faced the media ahead of the game, and provided an update on the progress of the Belgian. They may be out the Carabao cup but they went out swinging and fighting till the end. Our defence wasn't as good as other times.
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I hope things will clarify as soon as possible". "Of course I know, I'm aware of what's happening, and it's sad, of course". I'm excited", he added, after winning the Swiss indoor championships in Basel on Sunday.
There were more errors and a few signs of promise from Tomori who was good on the ball and strong in the tackle but perhaps a little too eager to impress after that early blunder, often rushing into areas that left his more experienced - and slow - centre-back partner Keogh exposed. "We were lucky on occasions".
Chelsea's game against Derby County can be viewed by United Kingdom residents on Sky Sports Main Event and Sky Sports Football, which are channels 401 and 403 respectively on Sky and channels 501 and 503 respectively for Virgin Media users.
"On another day, they go in but we've come here, done fantastic as a team, it shows where we are at and how confident we are on the road so I'm very happy, but disappointed we've lost at Stamford Bridge".
"It is important that we have a lot of players who can score goals and decide games and I hope they can continue to taker their opportunities". I joke because I'm proud.
For the first time in his fledgling managerial career, Lampard will be in the opposition dugout against the club where he won 11 major trophies - including three Premier League titles and the Champions League. "My overriding feeling is thanks to the fans of both clubs, and pride in the team".
The 19-year-old has dazzled in the Championship so far this campaign in Lampard's team and is being tipped to become a future first teamer with Chelsea.