The Blues navigated a tricky all-west London encounter after an own goal and a Jorginho penalty fired them to a 2-0 win at the Brentford Community Stadium.
They were immediately paired with Spurs and boss Tuchel said: "It was clear it was always going to be a strong draw, with four tough teams, but Tottenham is nice for our fans. It's a London derby and were looking forward to it."
With his squad still ravaged by Covid-19, Tuchel handed debuts to academy prospects Harvey Vale, Jude Soonsup-Bell and Xavier Simons for their last-eight meeting with their neighbours.
But it was substitutes N'Golo Kante, Reece James, Mason Mount and Jorginho who turned the tie in Chelsea's favour.
Kante, who Tuchel had maintained would not be involved due to his lack of fitness, provided the spark behind their opener 10 minutes from time.
The midfielder's quick feet on the edge of the area evaded a couple of Brentford challenges before he slid in James, whose cross was bundled into his own net by Pontus Jansson.
Three minutes later Mount was clumsily tripped by Brentford keeper Alvaro Fernandez and Jorginho fired the Blues through.
"We had a brilliant performance and a brilliant result, given the circumstances," added Tuchel.
"We were very disciplined, very structured and had individual quality. Well done to the boys. I'm super happy.
"The three boys did well. They did not train for a week because the academy was closed, then we invited them to train with us for two days.
"They listened carefully and did their job. And the seven guys that played with them supported them. They did well and were involved in a good performance."
Defeat meant the Bees missed out on a second successive semi-final in the competition, against the side that beat them last season.
Boss Thomas Frank said: "According to the game plan we gave nothing away and they couldn't find a solution, and we had by far the best chances in the first half. So first half, tick! We should have been in front.
"But in the second half we struggled to create anything. We defended well and gave nothing away until the 80th minute, when we needed to do better.
"Pontus will blame himself but he's had a fantastic season. Two minor mistakes gave them their goals and that was the difference today."