Spurs made an impressive start to the season, overcoming the departure of star striker Harry Kane to Bayern Munich by topping the table early last month after winning eight of their first 10 Premier League games.
And after watching his side suffer a 2-1 defeat to David Moyes' team, Postecoglou said on Friday: "A brilliant start last night would've been taking advantage of the dominance we have in games. But we're not. It's keeping oppositions in the game and especially in the second half we had a couple of defensive lapses and a team like West Ham will always punish us.
"For the football to be brilliant, it's got to be there in its entirety and I don't how many times I've said, I still think in our front third we've got a lot of work to do.
"Unfortunately that's costing us at the moment in terms of results. That's the challenge for us, we've got to keep pushing on and try to become better in those areas.
"For me, I don't have a three or five year plan up my sleeve that's guaranteed for success, what I do have is a plan that I think will get us to where we need to be. How long that takes, I don't know.
"It depends on how we keep discipline in staying and sticking [to] the path. Ultimately whether it's this challenge there'll be another challenge in six months, there'll be another one, even if you have success there's a challenge there.
"It's how focused you are and how committed you are to go on the path you've started. I'm not wavering with that, I just will not budge. I just think that's what I believe is the best way forward."
Spurs have rejected an approach from Swansea City for assistant coach Chris Davies but Postecoglou suggested there was still a chance he could leave.
"I've had a brief discussion with Chris and he knows we've got a busy week so we'll focus on that," said Postecoglou. "He's an outstanding individual, he's done some great work with us and great work in the past. It's not surprising to me that Swansea or other clubs would look at him. It's what you want to be honest.
"You want good people and when you've got good people they're going to attract attention. From my perspective, whatever that transpires to, it's very much in Chris' hands. It's his decision in terms of what he wants to do moving forward and obviously the club will deal with it from there."
Howe turned down the chance to manage Celtic prior to Postecoglou taking the job, where he thrived in two seasons before succeeding Antonio Conte at Tottenham.
"Oh [it was] absolutely [a] sliding doors moment," added Postecoglou. "There's probably been no bigger decision in me being here today than Eddie knocking back the Celtic job. I haven't thanked him, I probably should."