The Blues lifted the Champions League after beating Manchester City in Porto on Saturday.
The Blues claimed their second Champions League title nine years on from defeating Bayern Munich on penalties in 2012.
Tuchel was right in the thick of the Blues’ celebrations, wildly dousing his players in champagne in the Estadio do Dragao changing rooms, and that after hyping up the Chelsea fans all night on the touchline.
The Stamford Bridge club’s partying will continue for the next few days, but then Tuchel will demand his players return to a feeling of never being satisfied in a bid to build a west London dynasty.
“The level is set, it’s set from us; and once the celebrations are over, once we all digest this experience, it’s the moment to grow, to evolve and use it to become better and learn from it,” said Tuchel.
“It’s absolutely crucial. But a lot of young players had this success, and now it’s a big, big challenge to stay hungry and go for the next one.”
Tuchel inherited a talented but directionless squad when replacing Frank Lampard on January 26 at Stamford Bridge.
The former Paris St Germain boss has transformed the Blues from a disjointed bunch into European champions in just 124 天.
But the taskmaster 47-year-old still insists Chelsea must “close the gap” on runaway Premier League champions City.
The summer signing of a marquee striker would certainly help that cause, with the Blues strongly interested in bringing Romelu Lukaku back from Inter Milan for a second stint at the club.
Timo Werner’s run off the ball created the space for Havertz’s winning goal, but the Germany forward also missed two gilt-edged chances to cap a frustrating campaign on the finishing front.
Recruit a regular goalscorer and Chelsea will be a major threat for sustained success, especially given the stunning defensive solidity ushered in by Tuchel.
Under Lampard the likes of Antonio Rudiger and Andreas Christensen appeared tentative and twitchy, whereas under Tuchel they have shut down the best attacks on the continent.
“Obviously we have a strong bond, a strong group who can really defend, and that’s a huge part of football,” said Tuchel.
“We can defend, and play, and answer all questions in the game.
“They have a huge energy together and can deliver under pressure.
“But we have to go for it again, we have to work hard and work to improve.
“We managed to close the gap on City in individual games in this season, and we did it here when it mattered hugely.
“But next season we still have to close that gap in the Premier League, and we have a big job ahead of us.”