The Socceroos made a rocky start and went 2-0 down within the first 15 minutes of their FIFA World Cup opener in Cuiaba, but pulled a goal back through talisman Tim Cahill and they had Jorge Sampaoli's men worried throughout much of the second half.
A third goal from substitute Jean Beausejour made the result safe for Chile in the Group B clash at the Arena Pantanal.
But Postecoglou and his players have every reason to hold their heads high, having pushed the South Americans all the way despite being written off before the game.
"If anything I thought if we got the second we'd go on with it," he told SBS.
"(It's) disappointing for the players. After a rusty start, which is understandable, I thought we were well in the game.
"They've got some quality players and at the start they were at their sharpest. We probably just gave them a little bit too much respect.
"I think once we got the first goal we got a bit of belief in ourselves and started pushing on a bit more. We kept the ball a little bit better although I thought even there we just lacked a bit of composure at times.
"I think we gave them a two-goal start and in the end that's what killed us."
With the Socceroos having been tipped to struggle in all three games, Postecoglou dismissed suggestions Cahill's goal would provide his players with additional belief, insisting they were already confident ahead of the tournament.
"We had belief going into it," he said.
"I've seen how hard these guys have been working. That's why we're disappointed. We really thought we could get something out of this game. The fact that we've lost 3-1, we've just got to take that bitter pill.
"Certainly moving forward, we'll get stronger."
Earlier on Friday, the Netherlands stunned reigning champions Spain with a thumping 5-1 win in Salvador, but Australia's coach is not daunted ahead the Socceroos' meeting with Louis van Gaal's men on Wednesday.
"It's a massive challenge," he said.
"We'll go out there and try and match it against the Dutch as well."
