The result has the Socceroos neatly positioned to progress to the World Cup with a win in Wednesday's home tie where they'll start favourites.
Postecoglou's side sparkled in San Pedro Sula, creating several gilt-edged chances without converting any for a precious away goal.
The performance came in stark contrast to the disjointed efforts in last month's Asian playoff with Syria, which Australia ended 3-2 on aggregate after extra time in the home tie.
Postecoglou credited his team with overcoming tough Honduran conditions but let loose when asked if he was expecting the home side "to be so easy".
"Maybe you thought we were going to be easy," he said.
"I saw the newspaper today, it had 11 kangaroos out there but kangaroos can play football, huh?"
The comments continue a war of words.
Australian media had said the match was being held in the "murder capital of the world" and likened the encounter to a game with ISIS.
The Central Americans replied, painted the tie as 'Operation Cangeru' and labelled Australia a simple team.
Postecoglou acknowledged wrongs but defended his team.
"When we got here, some people made some comments about the country and Honduras and that was wrong and we apologise for that," he said.
"I also think there were some comments about our team coming from the other side that were disrespectful.
"We had two players that play in the Premier League out there. They play in first divisions in Europe and all I heard is we have a simple game plan and we don't have any stars.
"That was our motivation. We do our talking when the game starts.
"We're expecting a tough game in the second game. We always respect our opponents. And we'll be ready."
Postecoglou rejected another view that the 0-0 scoreline advantaged Honduras, given they can progress with either a score-draw or a win.
"If you think they've got the advantage after us coming here and playing in these conditions and dominating the game, then you've got a different view of life than I have," he said.
"We played well tonight.
"We were missing the final chance to score the goal (but) if we play like that at home, especially with fresh legs, we'll score."