“I said to the lads that everyone had written us off. We needed the lads to show bravery on the ball and they did,” Lampard told Sky Sports.
“We have to enjoy the moment but now prepare for Aston Villa, but we’ll be underdogs again.”
Leeds boss Marcelo Bielsa, speaking via a translator, was left regretting his side’s failure to make the most of their first-half dominance.
“We should have made a bigger difference in the first half,” he said.
Leeds were a man down 12 minutes from time when Gaetano Berardi was sent off, with veteran Argentine manager Bielsa adding this had made the game “unbalanced”.
Wednesday’s match between two of English football’s leading clubs of the early 1970s came after Leeds’ defeat of Derby in January was overshadowed by the ‘spygate’ affair that saw Bielsa admit he had sent a staff member to ‘spy’ on a Rams training session before the game.
Leeds took a 24th-minute lead on the night through Stuart Dallas after Kalvin Phillips’ free-kick hit a post.
Derby though scored just before halftime when substitute Marriott capitalised on a mix-up between Leeds defender Liam Cooper and goalkeeper Kiko Casilla moments after coming on.
They drew level on aggregate straight after the break when Harry Wilson played in Mason Mount, who cut inside from the left and beat Casilla.
Derby then went ahead in the tie for the first time in the 58th minute when Cooper needlessly conceded a penalty following a pull on Mason Bennett in the area, with Wilson scoring from the spot.
Derby’s 3-2 aggregate lead did not last long, however, with Dallas scoring his second goal of the game when he struck a precise shot into the far corner.
Leeds were reduced to 10 men when Berardi’s reckless two-footed challenge on Marriott saw him sent off.
Derby’s winner arrived in the 85th minute when Marriott charged through on goal and dinked over Casilla just before the keeper could get to the ball.
Scott Malone was then sent off in stoppage time but his exit did not allow Leeds to snatch a late leveller.