Arsene Wenger's side were emphatically ejected from the Champions League on Tuesday after a 5-1 humiliation at the Emirates, a result which saw a final aggregate score of 10-2.
The Irishman also had his say on Sanchez, who was criticised after the game for appearing to laugh following his substitution.
"I think certainly the last half an hour or 35 minutes they gave up. There’s no forgiving that." Keane told ITV.
"There’s no shame losing to Bayern but there is when you down tools for the last half an hour and you lose 10-2. It was shameful.
The Republic of Ireland assistant manager continued: "I thought they were shameful the last half an hour. The goals they were giving away and people not running back.
"Yes they played really well in the first half but gave up in the second half. At this level, at any level, it’s ridiculous.
"You can talk how much you like but you’ve got to show how much you’re behind your manager when you’re on the pitch for 90 minutes."
One player who came in for severe criticism after the game was Alexis Sanchez, who drew the ire of supporters for appearing to laugh following his substitution, with the game over as a contest.
Keane had no sympathy for the Chile international and believes that the Gunners hierarchy should do everything they can to speed up his exit.
He said: "On the topic of Sanchez... If you’ve got players at your football club who don’t want to be there then get them out of the door.”
Arsenal return to action on March 11 when they host non-league Lincoln City in the quarter final of the FA Cup.