Former Paris Saint-Germain boss Tuchel took charge at Stamford Bridge against misfiring Wolves less than 24 hours after replacing the sacked Frank Lampard.
Club owner Roman Abramovich handed the 47-year-old a brief to revive the fortunes of a team that had lost five of their previous eight Premier League games.
Chelsea struggled to make an impression against Nuno Espirito Santo’s men, whose form has nose-dived after forward Raul Jimenez fractured his skull in late November.
The home side dominated territory and possession, but created few clear-cut chances and the visitors had opportunities to leave with all three points.
The new Chelsea boss did not appear downhearted despite the flat display.
“I was very happy performance-wise,” he said. “Unfortunately we couldn’t score. If we take care of our performance like this the results will come.”
The draw lifted Chelsea to eighth spot, five points behind fourth-placed West Ham but Tuchel knows time is not on his side, with more than half of the season gone.
He admitted he had not yet been able to properly assess his squad.
“It was today totally unfair because I had no explanation for anybody on the side why they didn’t play,” he said. “Every day will help.”
