The 28-year-old utility back will not feature in the 22-man squad for Saturday’s meeting with South Africa in Sydney, despite racking up 92 caps for his country.
Former Australia coach Eddie Jones told The Sydney Morning Herald: “I think the whole thing is quite sad to be honest.
"If I was a supporter, the one player I'd be happy to pay money to see would be [Giteau] - he gives his heart every week.
"Right now, for some reason, Robbie doesn't see him as the answer at number 12."
Australia’s 2007 coach John Connolly echoed Jones’s comments and claimed that Giteau’s aggressive play will be missed.
"I've coached first-class rugby for 20 years and two people spring to mind for what they bring to team [in toughness] - Matt Giteau and Tim Horan," Connolly explained.
The player's absence this weekend may affect his chances of being called up for the World Cup in New Zealand this September.