The new man in charge saluted his players' efforts after they worked hard to register a narrow victory in his first game as head coach of the national team
A Tim Cahill header in the 69th minute ensured Postecoglou made a winning start to his reign against the 31st-ranked Costa Ricans.
The coach concedes the Socceroos lacked fluency at times as they adjust to his new system but could not fault the effort of his charges after dominating possession and creating the bulk of the chances.
"I couldn't fault the players' endeavour or their willingness to embrace what we're trying to do, they were fantastic so I'm pleased they got the rewards more than me because they've worked really hard this week," Postecoglou said.
"It was obviously our first time together and we're trying to adjust the way we do things and full credit to them and I guess the goal gives that reward and hopefully some belief moving forward.
"They didn't take a backward step tonight against a very good team and really they only created one or two opportunities the whole game and that was because our pressure and our discipline was fantastic and there were times where our football was also equally good.
"I think that was a performance that everyone can take pride in, particularly the players."
He says the Socceroos have now set the minimum standard they must now meet every outing and insists he is not scared of the increased expectations he knows will now come from Socceroos fans.
"Let them get carried away, like I said before I took the job, I don't think we're about talking ourselves down and I'm not afraid and I don't think anyone else should be," he said.
"Ultimately I'm the one that if we don't make giant strides ahead I'm the one that's going to take that responsibility and I'm not afraid.
"I said at the start of the week I wanted to leave this camp with belief in the group and belief in the nation that we're going to be better moving forward.
"If it raised people's expectations that's great, I've certainly got high expectations and I want everyone else to as well."
The new coach was reluctant to single out individuals but heaped special praise on fullbacks Ivan Franjic and Jason Davidson after a solid defensive performance.
"I thought our football was ok and we'll get better but our defensive pressure was first rate," he said.
"We were at them the whole 90 minutes and I wanted us to take the game to the opposition.
"We were at home and I thought there were promising signs there in terms of what we're trying to build and that kind of sets the standard for us now moving forward.
"We want to better than that next time and it's not a bad place to start."
Meanwhile, Costa Rica coach Jorge Luis Pinto said the Socceroos proved they can play but lamented the absence of key personnel through injury.
"There's no friendly games and I was very happy with the way Australia played football, they knocked it around, they kept possession without risk," Pinto said.
"We knew we were going to struggle because some of our best forwards are not here but nevertheless this is all just preparation for the World Cup.
"I'm very happy with the way the team went, I though it wasn't the best performance from the referee but I was happy with the performance keeping in mind the players I had."