Thomas Tuchel's first game as Bayern Munich coach may have been an impressive 4-2 victory over rivals Borussia Dortmund, but he knows there is work to do.

Tuchel replaced Julian Nagelsmann during the international break, and his first game in the dugout was Saturday's Klassiker against his old club Dortmund, who had won nine of their first 10 league games in 2023 to leave them top of the Bundesliga.

But Bayern leapfrogged them to the summit in style.

Gregor Kobel's error and a Thomas Muller double had the 10-time reigning champions 3-0 up within 23 minutes.

Kingsley Coman made it 4-0 shortly after half-time, and though consolation goals from Emre Can and Donyell Malen somewhat took the shine off their victory, Bayern now look the clear favourites to claim an 11th straight Bundesliga title, with Opta rating it at an 87.7 per cent chance they become champions again.

Despite the great start to his tenure, Tuchel insists there is still much work to do if Bayern are to get where he wants them to be, telling Sky TV: "I was very nervous today. It was a good first step but there is still a lot of room for improvement.

"It was a bit too wild, we wanted to have more dominance. We started very nervously. The whole game was actually too sloppy with too many ball losses.

"We have a lot to analyse. The team is extremely willing to learn. I understand that some things haven't worked out yet. All in all, it was too many turnovers that made life difficult for us. We want to be in possession.

"It's a bit like a band or an orchestra. We have to find our rhythm."

Nagelsmann's sacking came despite Bayern being in the Champions League quarter-finals.

"Everyone was aware of what was at stake here. A change of coach always brings unrest, there was a lot to absorb," Tuchel added.

"The will to implement everything was there 100 per cent. That's the most important.

"When we played calmly and clearly, we had top-class chances. We have leaders, and that will give us peace and confidence."