Scharner and the Austrian FA (OeFB) gave different accounts of events surrounding the 32-year-old Hamburg SV defender.
"Even before I arrived, it was clear in the Austrian media that I would no longer be playing against Turkey or in future," said Scharner on Hamburg's website.
"I said I cannot accept this role and therefore I cannot make myself available as that is the coach's job," said Scharner. "Koller then told me I would not play under him again."
The Austrian federation said Scharner had demanded a key role against Turkey and walked out of the team hotel when he was not promised it.
"Paul has started twice recently and we have several options, particularly in the centre of the defence, which is why I wanted to use the game to try out something else," said Koller.
"Since he could not accept this, he decided to go home."
Scharner described the OeFB's version as "absolutely inaccurate".