The England skipper was part of the side of were beaten 5-1 by Eintracht Frankfurt in the German top flight, their first league defeat of the season.
With the club already losing the German Super Cup and being eliminated from the DFB Pokal by a third tier side, Bayern now sit four points behind league leaders Bayer Leverkusen, albeit with a game in hand.
Thomas Tuchel spoke after the game, saying: "If you have a week of preparation, you don't have many arguments on your side. We have deservedly lost, even this heavily.
"It was too much today and we were punished severely. We definitely weren't ready, everything went against us very quickly.
"The willingness, the energy that it takes to win away games was not there. We pointed this out to the team several times, but the message didn't get across.
READ MORE ON HARRY KANE
Harry Kane and Co refuse to speak after Bayern humiliation, but Man United get warning
Harry Kane's trophy hopes take another blow in historic Bayern Munich humiliation
"We have to take a look at ourselves. The team's performance today is inadequate - and I'm part of the team."
Bayern's stars, however, had been notably quiet in the aftermath of their 5-1 win., But on Sunday Kane addressed the defeat with a short post on X.
He wrote: "We know yesterday wasn't good enough and full focus now on Tuesday to show the right reaction."
Next up for Bayern is a Champions League Group Stage clash with Manchester United at Old Trafford on Tuesday.
Most read in Football
Fans spot bizarre error on Brennan Johnson's Tottenham shirt during Newcastle clash
Reece James forced off injured AGAIN during Chelsea's game at Everton
West Ham fans have nightmare trip to Craven Cottage as boat crashes into a bridge
Ian Wright stunned Roy Keane with his Man United v Bournemouth prediction that came true
Man United must beat Bayern, who have already won Group A, to stand a chance of going through but will also need Copenhagen and Galatasaray to draw their showdown.
The Red Devils go into the clash off the back of an embarrassing result of their own having suffered a 3-0 hiding at home to Bournemouth on Saturday.