The wing-back was impressive for their 2-2 draw at Arsenal.
Postecoglou said: "I thought both our full-backs had difficult jobs. Arsenal's wide players are outstanding players and that's where their threats are.
"Destiny getting booked early, it could have made it difficult, but the way he dealt with it, in the end I thought he was the dominant player on that side of the pitch. He finished really strong and had to contend with having a yellow card.
"It's a great learning experience for him and for all the guys. They've come through that, going toe to toe with a top side. There's a real will and desire to become the team we want to be, which includes making sure that you're disciplined and you're buying into the team ethos and we had a really young team out there.
"Vic, that's his first derby, Destiny, van de Ven, Pape Matar Sarr, Brennan, they're all in their early twenties, Porro, even Kulusevski is only 23, so it was a young team but just super proud of the experienced players we did have in there. Romero was outstanding, Bissouma has been brilliant all year, Maddison, and Sonny was just on a different level, not just his goals, although they were outstanding, but his work rate, his work ethic was incredible."