Under-fire McKenzie has been the subject of speculation about his private life and player discontent in the Wallabies camp.
Gutsy Australia were seconds away from victory in Brisbane before a last-minute try from Malakai Fekitoa.
Australian Rugby Union chief executive Bill Pulver said in a statement: "I did not ask Ewen to resign, but understand his decision.
"He informed me this morning of his intention to resign, regardless of tonight's result."
McKenzie has denied claims that he was involved in an intimate relationship with a female staff member who resigned last week.