Bayern Munich chairman Karl-Heinz Rummenigge slammed Borussia Dortmund fans for their "ingratitude" towards Mats Hummels during the DFL-Supercup on Sunday.

Hummels made his competitive debut for Bayern in their 2-0 victory over his old club, with goals from Arturo Vidal and Thomas Muller sealing the win for the Bundesliga champions.

Germany international Hummels was booed with every touch of the ball by large sections of the crowd at Signal Iduna Park, many of whom have not forgiven him for leaving Dortmund for their title rivals in July.

But Rummenigge has blasted those fans for failing to recognise the efforts of the 27-year-old during his Dortmund career, in which he won two Bundesliga titles, two Supercups and the DFB-Pokal.

"Ingratitude is the world's wage," he said. "It's a disaster that someone who gave everything for the club for years is booed like that - it's so disappointing."

Hummels admitted that it was a peculiar sensation to step onto the pitch as part of Dortmund's opposition, but said there are plenty of fans who remember him more fondly.

"I was caught out when I felt so emotional before my entrance into the stadium. It was a strange situation," he said, as quoted by Bild.

"You can treat the subject as you wish. There are also a lot of very positive things still. I still see people write on Twitter and Facebook, who value our time together. To them, I try to respond to say that I see it that way."

Hummels hopes there is more to come from him at Bayern after conceding that his extended break following Euro 2016 has left him playing catch-up in terms of fitness.

"It is the first title but my performance could be better," he said. "But if, after only eight days of training, you were at the same level as those with five weeks of training, then pre-season would be nonsense.

"For me, it was an important game to make a step forward concerning my fitness. Regarding my performance, that was hopefully not the top limit."