Klose sealed a crazy 2-1 victory for the Germans in the 89th minute when he nodded in a cross from Ivica Olic.
Klose said: "Eh, I had the sensation of being in an offside position. But the referee didn't blow his whistle and I did my job."
Bayern coach Louis van Gaal was even more brazen about the nature of Bayern's result.
"It's true, we scored two goals and one was clearly offside.
"In modern football you cannot judge anymore without the help of technology, because a referee cannot see everything with his assistants.
"At times, they just can't do it. I have been saying so for 10 years.
"Bayern were penalised against Bordeaux. It happened once to us and now to the others. But this is football and it needs to be said that the referees can't see everything.
"They need to be helped."