Chelsea beat Championship side Middlesbrough 2-0 to advance to the FA Cup semi-finals on Saturday.
The victory was Chelsea's fifth in succession across all competitions since owner Roman Abramovich's troubles with the UK government placed the club in disarray.
Chelsea are bracing themselves for a new owner in the coming days.
Sanctions imposed on the club meant less than a thousand Blues fans made the trip to the Riverside stadium as they were unable to sell tickets while Middlesbrough had a full house.
The game was even more tricky given that the in-form championship side had knocked out Premier League opposition in Manchester United and Tottenham Hotspurs in the previous rounds.
Nonetheless, Tuchel has been impressed by how his players have responded.
"We were very focused and very serious from the beginning," Tuchel told BBC Sport.
"We showed quality in decisive moments and scored two early goals which gave us a comfortable lead, but the effort was huge to not allow big chances. I'm very happy, it was a very deserved win.
"I'm impressed with the players' focus. We accepted the [ownership] situation because we didn't cause it. It isn't in our hands, but it was important we showed the right spirit and took responsibility.
"This is very, very good. If you have the talent, it is a responsibility to show it."
