Despite making a bold start to the game, the Royal Blues collapsed as Bayern turned on the style to join Borussia Dortmund at the top of the table with a 4-0 win.
"Bayern are a top team who played cleverly, keeping the ball among their ranks and the difference in class today, particularly in the second half, was simply too great," said the Germany international.
"The two unfortunate goals we conceded out of nothing pretty much finished us off.
"It became incredibly difficult for us after and maybe we lacked a bit of energy to put them under more pressure up front."
Bayern coach Pep Guardiola admitted it was his side's "best Bundesliga game of the season".
"We dominated completely," he said to Sky television. "In other games, we've played well for 30 or 45 minutes, but this time, we did well for the entire 90.
"I'm proud of our performance and the game."