Benjamin Pavard says Bayern Munich fans can expect a successful season and should not fear any "little crisis" that comes the way of the Bundesliga champions.

Niko Kovac's side beat Real Madrid 3-1 in the International Champions Cup on Sunday despite goalkeeper Sven Ulreich's late red card in Houston.

There were encouraging signs of improvement following Bayern's 2-1 loss to Arsenal last Thursday, particularly with the DFL-Supercup showdown with Borussia Dortmund now less than two weeks away.

Bayern's domestic dominance looked under serious threat from Dortmund last term, but a strong second half to the season saw them claim the league title and the DFB-Pokal.

And Pavard, who completed his move from Stuttgart after the end of 2018-19, thinks there is every reason to be optimistic heading into the new campaign.

"We were strong, we defended very well, attacked very well," he said after the win over Madrid. "We scored three goals. We conceded a goal, which is annoying, but it does not matter. We just must remember the fact we won. We feel better and better.

"Of course, it's a very big club, which has a habit of winning a lot of titles. We know that if we lose one or two matches in the season, it's a kind of little crisis. But I don't worry: we really have a very good squad and a great atmosphere. It will be okay.

"I have a lot of confidence. There is a very good atmosphere. On the pitch, we can see that everyone takes pleasure. We are making every effort together."

Bayern face AC Milan and Fenerbahce in their remaining pre-season games before meeting Dortmund on August 3 at Signal Iduna Park.

They then take on Energie Cottbus in the first round of the DFB-Pokal before getting their Bundesliga campaign underway at home to Hertha Berlin on August 16.