We need to stamp our authority in that and kick on. Seven points from nine have propelled Derby back into the play-off positions and Waghorn wants to continue that form and climb the table.
Keogh nearly equalised in the 84th minute when Tom Huddlestone played a sublime ball over the top, while Nugent thought he had scored but saw his shot rebound off the inside of the post.
Davide Zappacosta's cross deflected in off Tomori's standing leg as Chelsea took the lead.
"There wasn't a tear in the eye, but it was emotional", Lampard said.
He is the club's record goalscorer with 211 goals and won 11 major trophies during his 13 years at the club.
After several frights, Maurizio Sarri tweaked his defence, bringing on David Luiz and dropping deeper which saw the home side eventually grind out the win - to make it 15 unbeaten games in a row.
Lampard has already seen off a former friend in the competition, beating Jose Mourinho's Manchester United side on penalties at Old Trafford and has started managerial life off well winning 10 of his 18 matches in charge so far.
'We scored four, didn't we?'
Chelsea assistant boss Gianfranco Zola said: "I thought Gary and Christensen could have done better in the first half". They may be out the Carabao cup but they went out swinging and fighting till the end. It looks like they're in good hands. Mount also went close late on and the huge travelling support bounced with pride throughout the 90 minutes. "We were lucky on occasions".
Lampard added: "I'm proud of them".
"I think we deserved a draw but I'm not upset at all".
"They've got players who showed they'll be more than capable of holding their own if they come up to the Premier League".
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.
"I sort of slipped out the back door when I left. I'm sure he'll be up for it and it will be important to get even more indications for us".
Cahill's future at Chelsea is being called into question and he certainly didn't perform with the consistency of old during the Derby game.
It will be the Blues' third match in the space of six days, having beaten BATE Borisov and Burnley in the Europa League and Premier League respectively.