Son started on the evening ahead of Wednesday's Europa League final against Manchester United in Bilbao.
Postecoglou said afterwards: "Well he's ready and he's available. He started today.
"They're all ready to start so I think him playing 70-75 minutes today was important and you could see he opened up a couple of times and I think he's feeling... it's as much about Sonny himself, and feeling that he's getting back into a rhythm and I think there were moments tonight where he showed that."
On the lift Son's return has given the dressing room, the manager also said: "It's important, especially when we've lost some key players in recent times.
"Madders (James Maddison) is also one of the leaders, and Deki (Kulusevski), and Lucas (Bergvall) in the last three weeks. Now getting Sonny back at least gives us another experienced player. I think the last two or three fixtures our average age has been three or four years younger than the opposition. You can see that at times so just having another experienced player available is great for the team."
Sarr and Moore okay
Postecoglou also commented on the injury picked up by Pape Matar Sarr on the night.
He added, "Pape felt something in his back so we took him off as a bit of a precaution. I don’t think it’s anything too significant speaking to him afterwards but he just felt something in his back and I think Mikey (Moore) was okay.
"It was fatigue as much as anything else. He hasn’t played that sort of amount of minutes before. "