The coach felt his players deserved to take something from a hugely entertaining contest, which was decided by the intervention of super-sub Memphis Depay
Having been somewhat unfortunate to lose 3-1 to Chile in their World Cup opener last week, the Socceroos defied expectations again in Porto Alegre, coming from a goal down to lead 2-1 before ultimately succumbing to a 3-2 defeat.
Up against a Dutch side who thrashed holders Spain 5-1 in their first outing in Brazil, it was another hugely impressive showing from a team written off before the tournament, but that was little consolation to Postecoglou.
"Yeah, it's still bitterly disappointing," he told SBS after the game.
"Just for the players, they were magnificent. They took it to a world class team. It's easy for me to talk about going forward and having self belief. But they're the ones that have to do it. Full credit to them. But I just feel bitterly disappointed they weren't able to get some reward out of it today."
Van Gaal surprised many observers by persisting with the reactive formation that worked so well against the Netherlands, but that only served to invite Australia to press relentlessly at Estadio Beira-Rio.
It was a tactical gift gratefully received by Postecoglou, but one he doesn't expect to be repeated by other opponents in the years to come.
"People look at us and sort of predict the kind of way we're going to play," he said.
"But we'll change those perceptions over time. I said to the players, today was about trying to play our kind of football. And if they're going to underestimate us, we have to make sure we punish them. I thought we were really good, first half we were excellent. We gave them one chance and Arjen Robben's a world class player.
"I can't fault the players ... I really want us to be an exciting team but it's the players who have to do it. They were magnificent."
Tim Cahill scored arguably the goal of the tournament to draw Australia level but will miss the final match of Group B against Spain after picking up his second yellow card for a challenge that left Bruno Martins Indi with a concussion.
"Timmy was magnificent again, he led from the front," Postecoglou said.
"I thought Mile (Jedinak) was outstanding. Bresc (Mark Bresciano) was really struggling physically but gave it everything. All the senior boys have been fantastic but we haven't made one excuse about players missing.
"Even today, we went out there and we said we'd have a go. And we did. And we'll do that in the last game. Timmy'll miss out but somebody else'll get an opportunity. And they'll show the same endeavour that the other lads have shown."