The two-time winners lost at Dinamo Zagreb in the first game of the group stage.
The Croatians have a poor record in this competition, having won just five of 43 games before this meeting.
The dangerous Mislav Orsic netted the 13th-minute winner, running through from the halfway line and finishing past the goalkeeper Kepa Arrizabalaga.
Arrizabalaga tipped the ball onto the bar as Dinamo came close to a second.
Pierre-Emerick had a goal ruled out for being in an ineligible position, but he looked off the pace.
The Albanian had little impact on the overall performance of the team.
The hosts were relieved to see James' low shot rattle the foot of the post with five minutes to go.
In the other game of the group, AC Milan travel to Salzburg.
In the first transfer window under the new owners, the club spent close to $300 million on new players.
After taking charge of the side for the 100th time against Dinamo, the German will need to work out his side's problems with the new owner.
Tuchel's success in his first few months at the club was due to a strong defensive platform.
In seven games this season, the Londoners have lost three times and kept just one clean sheet.
The defensive team-mate of Kalidou Koulibaly was making his first appearance in the group stage.
The lack of understanding between the pair was obvious for the goal when they both went for a high ball.
It allowed Bruno Petkovic to flick the ball on for Orsic, who held off Fofana before moving to goal and scoring with a cool finish.
Arrizabalaga, who started instead of Mendy, denied Ristovski with a save.
At the other end of the field, Pierre-Emerick Aubameyang was given his first start since signing from Barcelona and he wore a face mask because he had been involved in a violent robbery at his home.
He ran through early on, but failed to pick out a teammate with his cutback and struggled thereafter.
Slow build-up play did not do enough to get a well-organised and obdurate Dinamo back line.
Kai Havertz's goal was blocked by Robert Ljubicic and Mason Mount's first-time strike was saved by Croatia's goalkeeper, but the visitors were still able to score.
It was Dinamo's first victory in the group stage, but it was their second defeat.
The perfect start from the Croatians gives them hope that they can reach the knockout stage of the competition for the first time.
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