The Brazilian came off with a hamstring problem in their 4-1 win over Aston Villa last week.
While fans were hoping to see him back soon, Postecoglou confirms the injury is a long-term one.
Asked about a timescale, Postecoglou said: “Not really. I’m reticent to put it but he’ll be out for a significant amount of time. It’s a significant hamstring injury.
“He was very disappointed. We tried to take a different approach and he worked awfully hard on his rehab, his general fitness. He really trimmed down in terms of his conditioning. He was doing everything right. We eased him back in terms of his return to playing, tried not to overload him.
“But unfortunately he’s broken down again. He’s disappointed but ultimately we just got to keep getting him back and working with him to get back because he’s an important player.
“We saw last week the impact he had coming off the bench and setting up the goal for us. Disappointing for him, disappointing for us because we haven’t really had him this year. We’ll keep working with Richy to get him back.”