The Brazilian faces fresh competition from new signing Brennan Johnson, who has not been registered in time to play in this game.
Asked about Richarlison's goal ahead of the game, Postecoglou said: “I guess it stops people talking about the fact that he didn’t score. I was happy with his contribution.
“He probably wasn't at the same level as in the other three games but he gets a goal and people will focus on the goal. But I'm still looking at his contribution to the team and thinking about what Richy needs to do for us to keep improving as a team.
“But he's not the only one, all of them are in that boat. But anything that gives a player confidence is great, particularly for strikers - I get that. Because obviously that's what people focus on. But I wasn’t unhappy with Richy before he scored a goal.”