Celtic were without 11 players for stalemate in Paisley that left them six points behind Rangers in the title race with the suspended Carl Starfelt joining 10 injured men on the sidelines including star striker Kyogo Furuhashi and number one goalkeeper Joe Hart.
Furuhashi dropped back out of the side after returning from a hamstring injury to score a matchwinning brace in the Premier Sports Cup final win over Hibs at Hampden last Sunday, which has set the Japan international back.
According to Postecoglou, the 26-year-old is likely to remain sidelined for the trip to Perth, along with Hart, who was deputised by Scott Bain in midweek after also struggling to shake off an injury picked up in the cup final.
When asked whether any of his crocked stars will return for the last fixture before the early winter shutdown, the Celtic boss replied: “It’s hard to say. I don’t think so. There may be one or two who are close but at this stage don’t expect any significant change to the team that was out on Wednesday night.”
Postecoglou insisted Hart’s injury is not serious, adding: “He was just unavailable, injured from the weekend. He will probably miss Sunday as well.
“We will see how it’s going. After the break we expect quite a few back.
"There’s no doubt that we have had a really solid run of fixtures and been challenged by quite a significant injury list.
“Through that we have tried to maintain a certain level of performance and commitment which has been good up until Wednesday night when we were disappointed not to get the job done.
“There is still one more game, we have to be ready for it and perform at the levels we can.”