Spurs have not won silverware since 2008, although fans are dreaming of challenging for the title after winning 23 points from a possible 27 so far this season.
Postecoglou has relished his dream start to life in England, but eager to point out his new club should be competing for trophies every year.
The former Celtic boss said: “I didn’t come here to not be successful. This club has all the fundamentals to be successful. The expectations should be there.
“Part of the reason why there’s been this real desperation for a trophy is because they feel that’s the space they should be in. That is the expectation, that’s the reality, but what drives me isn’t raising or trying to dampen expectations.
“What drives me is trying to build something that will realise the ambitions that this club has at this particular moment. People’s perceptions don’t concern me too much. This is a big club and should be in a position to challenge for trophies every season in my opinion.
“At Celtic we were on top for a very long time but at the beginning when we weren’t on top, I don’t think people saw anything different in my demeanour. I don’t think they will (here).
“It is one thing I do. It’s not about staying kind of level-headed or getting carried away with either thing. It’s just that, my role in that context is to be the one thing that people can rely upon to be consistent.
“In that I have one objective all the time: how can we be better? When that is your objective, it doesn’t really matter where you are on the table or kind of what the outside noise may or may not be doing.
“It is about the players and the staff and everyone involved with the football club, looking at me. The one thing I do is I come in every day, I am buzzing about doing what I am doing. You know, that’s the kind of demeanour I have consistently.
“It’s just the way I am. I get so much satisfaction from what I do. I really enjoy what I do, on a daily basis. There isn’t a day I don’t get up and I’m not looking forward to the day ahead.
“There’s no other levels of satisfaction in me to get. That’s it. I’m buzzing to do what I do.
“Within that context I also understand that I have a real big responsibility to lead an organisation, players, staff, people to what I hope will be a successful place.
“There’s got to be some reliability there in what they see and what they feel with me so some of it is conscious but the other bits, I’m not skipping about the place but I’m really happy. I love what I do. Just the way I am. I’m very, very happy.”
Postecoglou’s happiness did not extend into the dressing room on Monday night after he criticised his players for a poor second half against Fulham.
It failed to stop the team blaring out Dolly Parton and Kenny Rogers’ classic from the 1980s’ of ‘Islands in the Stream’ following the 2-0 win.
But Postecoglou joked: “I stay out of the dressing room partly because of the music choices of the players.
“Most clubs want to turn their grounds into a fortress – ours is becoming a nightclub, mate. I’m all for it, whatever makes people happy that’s my thing.”
Spurs will assess Destiny Udogie ahead of the trip to south London after the left-back struggled with muscle tightness during the victory over Fulham.