Postecoglou dismisses talk that Spurs fans will want to lose against Man City
Mikel Arteta's Arsenal are one point above City at the top of the table, but Pep Guardiola's team crucially have a game in hand.
Arsenal, on 86 points, host Everton in their final match of the season on Sunday while City play West Ham at home.
It means if City win their final two games, they will secure an unprecedented fourth consecutive English top-flight title.
Much of the talk ahead of Tuesday's game has centred around whether Tottenham fans will want their team to lose in order to deny Arsenal the chance to win the league for the first time in 20 years.
But Spurs manager Postecoglou bristled at the notion that Spurs were focused on anything other than a win at his pre-match press conference on Monday.
"People are allowed to feel the way they do but I think I've been really consistent and really strong in my beliefs that it's important for this football club to get to where we want to, not look for a silver bullet," he said.
"It's hard work, perseverance, it's resilience, it's quality that will get us what we want, not to fall for any sort of false dawns or any short-term result reactions, stick to the course and thirdly, know what real success looks like.
"Real success looks like trophies. Anything else in between, bragging rights, whatever, it is absolutely meaningless to me... we've got a game tomorrow we want to win."
The former Celtic boss said he was confident that supporters would be behind Tottenham on Tuesday and that opinions online were not a good guide.
"If you go by social media there's probably 99 percent of Spurs supporters who don't (want to win against City), if that's your world but please don't tell me that's your world... we'll need to have a counselling session if that's your world," he said.
"I understand rivalry -- I was part of one of the biggest ones in the last couple of years in the world with Celtic and Rangers but I will never understand if somebody wants their own team to lose. That's not what sport's about."
Tottenham were early pacesetters in the Premier League campaign, but a late-season slump looks like costing them a place in the Champions League next season.
A win for fourth-placed Aston Villa against Liverpool later on Monday would end the club's hopes of qualifying for Europe's top club competition.