Scharner left the team hotel after a discussion with coach Marcel Koller on Tuesday afternoon.
Within hours, a statement on the Austrian FA's (OFB) website said that he "had demanded a key role in today's game and in the upcoming World Cup qualifiers".
Koller is quoted as saying: "Paul has started twice recently and we have several options, particularly in the centre of the defence, which is why I wanted to use today's game to try out something else.
"Since he could not accept this, he decided to go home."
Scharner has now given his side of the story on the website of his club, branding the OFB's version of events "absolutely inaccurate".
"It was clear in the Austrian media before I even arrived in Austria that I would no longer be playing against Turkey or in future," he said.
"Instead, he (Koller) told me that I was to move onto the players' advisory panel so that I could motivate and lead the team.
"This is a role I cannot accept and I am not going to make myself available for it. That is like taking a coaching role.
"After that, Koller said that I would never play under him again and that is why I left the team.
"This way, I can focus my full efforts on Hamburg."
Scharner has appeared 40 times for his country but the chances of him adding to that now look minimal, at least as long as former Bochum and Cologne coach Koller remains in charge.
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