Alexis Sanchez cancelled out an Arjen Robben strike to leave the two teams level at the interval, but Bayern scored four unanswered goals in the second period to record a 5-1 victory at the Allianz Arena.
Keane has said that Arsenal "have only got two decent players", and the former Republic of Ireland international did not see the humiliating loss as much of a surprise.
"They have only got two decent players and the rest are average," Keane told ITV Sport. "I'm not surprised. Did you think they would go to Bayern Munich and get a result?
"We have said it before – there is a lack of leadership, character, hunger and desire."
Arsenal are on the brink of elimination in the last-16 stage of the Champions League for the seventh consecutive season.