Head coach Postecoglou confirmed on Friday that the England midfielder will not play again until the New Year due to the issue being much worse than first thought.
The same is true for centre-back Micky van de Ven, who was forced off in the same game against Chelsea with a hamstring injury that his manager has confirmed is “severe.”
Asked whether the player who comes in for Maddison against Wolves on Saturday can do a similar job, Postecoglou replied frankly: “I don’t think you can replace him, but the system kind of adjusts to the individuals within it.
“We didn’t create a system for Madders. We had a system, and Madders fit into that - he brought his own qualities to it.
"Whoever we bring in to replace him isn’t going to be the same player, he’ll bring different qualities to it, but it won’t change our overall structure or intent in the way we want to play.
“It’s just there’s going to be some variances because of the nature of a different player being in there. I’m just disappointed for Madders.
"He’s had an unbelievable start of the season, he’s probably been one of the best players in the competition, and he was looking forward to striving for more. I’m disappointed for him that that’s been interrupted in the short-term.”
Maddison, who has three goals and five assists in the league so far this season, dropped out of the England squad on Friday due to his ankle injury.
Postecoglou took issue when asked whether the mounting injury list and defensive suspensions mean Saturday’s trip to Wolves will be the first real test of his reign.
He said: “The first test? Losing the greatest-ever player in this competition [Harry Kane] the day before the start of the season? Nah, piece of cake," he said. "We lost players to almost season-ending injuries - nah, don’t worry about it.
“There are tests all the time. In my whole career, I figured out there are only two states of being as a manager: under siege, or it’s coming. I’m well aware that every day, nothing runs smooth. There’s always challenges out there.
“It’s being a bit disrespectful to this group of players to say that everything has gone their way, because it hasn’t.
"From day one, there’s been a real resilience and character in the group and they’re going to have to show it again. It’s already there.”