Mats Hummels knows that substandard displays produced by Bayern Munich's players cost Carlo Ancelotti his job and says the squad is determined to make up for their recent shortcomings.

Ancelotti led Bayern to the Bundesliga title last season but was dismissed in September after a 3-0 loss to Paris Saint-Germain in the Champions League.

The Italian has been replaced with the familiar figure of Jupp Heynckes, who has been tempted out of retirement after four years away from the game.

Bayern are at home to Celtic on Wednesday as they seek to bounce back from that heavy loss at Parc des Princes, with Hummels among those to acknowledge the role of the players in a disrupted start to the campaign.

"We have certainly contributed to the fact that Carlo Ancelotti has been sacked after just 15 months," the Germany international told Bild.

"We had too few convincing performances… we were not able to get the top level constantly over several games, which annoyed us as a team.

"We definitely have to… improve in many things. [We are] not at the level at which [we] must be to belong to the absolute top teams in Europe right now, and this cohesion has yet to grow again. 

"We definitely have a lot of people talking in the locker room and trying to influence [it]." 

Bayern are second in the Bundesliga, two points behind Borussia Dortmund, while they trail PSG by three points in Group B of the Champions League.