They have made no secret of their desire to win the treble of Bundesliga, German Cup and Champions League with coach Pep Guardiola in the final year of his current contract.

“We are always hungry, which we saw again tonight,” said Bayern's sporting director Sammer.

Few teams will fancy facing Bayern in the knockout rounds but captain Philipp Lahm said it was important for his side to ensure they progressed in first place, thereby avoiding a last-16 clash with other group winners including Barcelona.

“It's always important to finish first,” said the ex-Germany skipper.

“It brings the advantage in the last 16 that you play the second leg at home. It's a good way to finish the year.”

But Sammer said he disagreed with Swedish referee Jonas Eriksson's decision to show Badstuber a straight red for bringing down Nigeria international Brown Ideye, who was through on goal, with 53 minutes gone.

“For me that was no sending off, I wouldn't have blown the whistle,” he said.

Badstuber will miss Bayern's final group match away at Dinamo Zagreb in a fortnight.

Meanwhile, Olympiakos remain second in the group, and a draw at home to Arsenal in a fortnight will guarantee that they go through at the English side's expense.

Germany defender Jerome Boateng said his side showed they deserve to be top of the group having also routed Dinamo (5-0) and Arsenal (5-1) at the Allianz Arena in Europe this season.

“That was again another concentrated performance from us,” said the centre-back.

“Being first in the group is important and was always our goal. We have confirmed today that we deserve to be first.”

The 27-year-old World Cup winner, who joined the Bavarian giants from Manchester City in 2011, has a contract with Bayern until 2018 but says he would be happy to extend that deal.

“I can well imagine that happening. I have always said I feel really well at Bayern,” he said.