Kulusevski headed home a 90th-minute leveller as Postecoglou's Spurs showcased their attacking quality with a 3-3 draw at Manchester City on Sunday.
Although they average two goals a game in the Premier League, the Australian's side are lowest scorers in a goal-laden top six and missed a succession of chances in consecutive defeats to Chelsea, Wolves and Aston Villa before drawing with the champions.
“We are still well short in that area," Postecoglou said ahead of the visit of West Ham on Thursday. "It’s still the area where we’ve got so much more upside in our front third to score more goals.
“I really feel like, apart from some areas where we need to keep working on, our front third stuff we’ve got so much more improvement to get to as a team.
“We’re seeing some of it at the moment. Brennan [Johnson] and Deki Kulusevski are starting to get a bit more familiar with their roles, and Gio [Lo Celso] getting a couple of goals from midfield. But I think it’s an area we can certainly improve."
Kulusevski said he felt like "the real me" after starting at No.10 in the games against Aston Villa and City, although he returned to the right wing for the second half at the Etihad and met Johnson's cross to earn depleted Spurs an encouraging point.
The Swede could be back in the front three against the Hammers, with Pierre-Emile Hojbjerg pushing for a start in midfield and Bryan Gil a candidate to drop out.
"I like him out wide," Postecoglou said of Kulusevski. "He can be a much bigger goal threat and we’re pushing him really hard in those areas.
"With his general energy and work-rate and his ability to break lines with his running, he’s probably more suited in my system to out wide but watching him centrally in the last couple of games he’s very effective in there and certainly an option for us."
One player who Postecoglou has no concerns about in the final third is Heung-min Son, who opened the scoring against City with a fine breakaway goal.
The Spurs head coach suggested the club is in the market for another centre-forward but says the "inspiring" Son should go down as a Premier League great.
"He's elite in every aspect," Postecoglou said. "I'd be very surprised if by the time he's finished, which is well down the track, he's not up there as one of the outstanding strikers because [although] a lot of his career has been played out wide but he's been a goal-threat the whole time.
"Now I'm putting him inside and that's why he's got nine goals already for the year. I think he's leading goalscorer for offside goals as well!
"Working with him every day, the example he sets, as a person as much as a footballer is just outstanding.
"It's inspiring for me when you see a person who, for all intents and purposes, has climbed a mountain many times in terms of his own football pedigree but every day, he loves what he does. Every day he feels it's a blessing and every day that rubs off on other people.
"Then he plays the game like that. He runs around like, he's literally just chasing balls down. That still inspires me, and I feel very grateful to be working with him.
"That [energy] is the definition of leadership. When the chips are down, when things aren't going well, everyone invariably looks at the leaders.
"What are your leaders doing? And I think he just got this thing in his head that whatever they say about me, good, bad, or otherwise, I'm not going to stop running throughout this period. And that has an effect on people.
"Through this period, where we've had to sort of dig deep and which we are still going through, he's been a force."
Spurs are likely to be busy in the January transfer window, with a new centre-half the priority but the club are in the market to strengthen throughout the squad.
Postecoglou continued: "Sonny will be a very important part of what we're building. And but that doesn't mean we wouldn't sign another striker because I think even Sonny would demand that of me.
"If you're going to build a team that's going to win things, I've always found your best players want more good players in the building."