A day after replacing Frank Lampard in the Stamford Bridge hotseat Tuchel was left with much to ponder as his side dominated possession but offered little goal threat.
Chelsea strung together almost 900 passes against a defensive Wolves but the vast majority were risk-free and easy meat for the visitors well-drilled rearguard.
An entirely forgettable first half at Stamford Bridge was followed by a more lively second period with Chelsea going close to giving Tuchel a dream start on a few occasions.
But Wolves had the best chance when Pedro Neto scooped a shot onto the roof of the net.
Chelsea’s poor run of form, which cost club great Lampard his job on Monday, continues and they have now managed to win only twice in their last nine league games.
Former Borussia Dortmund and Paris Saint-Germain coach Tuchel sent on Mason Mount, Christian Pulisic and Tammy Abraham late on and they livened things up but Wolves held firm to leave Chelsea in eighth place.
It was not the start Tuchel would have liked but after what he described as a “surreal” week he found plenty of positives from his side’s performance.
“I enjoyed it a lot because I was very happy with the intensity, the attitude, energy and quality of my team, we were well organised, had a lot of ball recoveries in the last third, never lacked intensity,” Tuchel said.
“Unfortunately we couldn’t score, but if we take care of our performance like this the results will come.”
The result left Chelsea eighth on 30 points, 11 behind leaders Manchester City, and Tuchel said he did not think his new side could make up that gap.
“The title? Wow. I don’t think so. We have to be realistic,” he said.
“When you sign for Chelsea as a player or manager, you sign for the expectation to challenge for titles … the Premier League, the Champions League and all the cups.
“At the same time, we have to be realistic. There are a lot of teams between us and fourth place, a lot of points between us. Maybe the best thing now, by stepping up in the middle of the season, is not to lose focus when we look too far ahead.
“Work on a daily basis on the details, on the progression in our game, and the points will follow. We have the capacity to hurt everybody in every competition. It’s my job to bring the team to its level as fast as possible. Step by step.”
Tuchel, twice a Ligue 1 winner with PSG, rung the changes for his first selection, dropping Lampard favourites Mount, Reece James and Abraham, and opting for experience with Olivier Giroud, Jorginho and Cesar Azpilicueta all starting.
There was lots of harmless passing in the first half but apart from an Antonio Rudiger header there was little to get excited about.
Tuchel clearly called for more daring after the break but it took Chelsea a long time to start to threaten, with Hudson-Odoi their most likely creator in a wide right role.
Tuchel waited until the 75th minute to send on United States international Pulisic and shortly afterwards gave Mount the chance to show that leaving him out was a mistake.
Mount looked impressive and one great turn almost resulted in a chance but his cut back found no one in a blue shirt.