The Socceroos banked 38 shots at goal to one from the Tajiks - a hopeful attempt from midfield which just snuck inside the corner flag.
"It was another positive step forward," Postecoglou said.
"It wasn't just that we won. I thought we played some really good football ... we played our style of game, we literally didn't let them out of their half.
"And apart from, if I'm greedy, some sloppy finishing, they were really professional."
The Socceroos will advance to the next stage of qualifying for the 2018 World Cup from top of their group with a win or draw against Jordan in Sydney on Tuesday night.
But finishing top means nothing to Postecoglou if it's not done in style.
"It's not about finishing top or winning games, it's about our manner and our growth as a team," he said.
"Top spot wouldn't mean anything if we're scrambling or scraping.
"If the aim is to qualify for a World Cup, the last coach qualified for a World Cup, he didn't even get there," he said, referring to the man he replaced, Holger Osieck.
"So what I'm saying is, the ladder position and the wins all need to be a consequence of us playing well. Otherwise they are meaningless."
Against Tajikistan, Postecoglou was most pleased with affording more opportunities to young players.
Greek-born striker Apostolo Giannou, on debut, had two goal assists and earnt two penalties.
Aaron Mooy, in his 12th game for the Socceroos, was the most influential player on the pitch; fellow midfielder Massimo Luongo, in his 18th appearance, was damaging and scored a goal.
Brad Smith (fifth cap), was industrious from left-back; as was Ryan McGowan (15th cap) at right-back.
Precociously talented Tommy Rogic (14 caps) came from the bench and scored two goals in three minutes; Nathan Burns (19 caps) also scored a brace.
"We gave opportunities to guys who I think showed they can be a part of it, even though the game wasn't very demanding or challenging," Postecoglou said.
" ... We just need to make sure we keep giving opportunities to guys so that we have a really good, strong squad that we can call on at any time."