The overall picture for Spurs has changed since they last played on April 13, with fourth-placed Aston Villa able to establish a six-point advantage while fifth is no longer set to provide Champions League football.
It does not decrease the significance of Sunday's clash at Tottenham Hotspur Stadium, with Arsenal aware a victory would move them a step closer to a first title in 20 years.
However, Postecoglou referenced his time in charge of Celtic when he looked ahead to a crucial fixture between two bitter rivals.
"Not in terms of that as a motivation, no," Postecoglou reflected.
"I want to win and I understand the importance of winning against your traditional rival.
"I've just come down from Glasgow. I've got a fair idea about what derbies mean to supporters.
"I never believe your motivation should revolve around the demise of somebody else.
"Your motivation should be about yourself. I want to win because I want us to achieve something.
"I want us to progress. I want us to be in a position fighting for the title. That's what drives me, not the demise.
"If that's your kind of measure, always peering over the back fence to see what your neighbour's building you could both have the worst houses in the street because everyone else is building beautiful places and you're looking over the back fence.
"I never wanted to win those games because it meant Rangers would lose. I wanted to win because I wanted us to win the title."
Tottenham have been inconsistent over the past two months but were still in the title mix as recently as March, according to Postecoglou.
The 58-year-old has made clear his desire for Spurs to challenge the likes of Arsenal and Manchester City next season and repeated that notion on Friday.
Postecoglou also rejected claims he would have accepted a fifth-placed finish in August when Harry Kane was sold, but did pay tribute to the squad for overcoming his departure with minimal fuss.
He said: "I was literally sitting in here the day before the Brentford game and he'd just left.
"I remember making a real conscious effort of looking really graceful above the water and if there was any panicking happening, making sure it was under the water so that nobody could see, particularly the players.
"Again, the players never batted an eyelid, which they could have, especially when you look at what Harry has done this year. It has been unbelievable.
"And yet he hasn't been mentioned as much as he would have been had we not been scoring goals.
"That's credit to the group, the playing group that they have embraced that challenge."
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