Postecoglou's side travel to Newcastle on Saturday looking to cement their grip on fourth place in the Premier League.
Tottenham are in position to qualify for next season's Champions League after they moved ahead of Aston Villa on goal difference last weekend.
Last season it was Newcastle who celebrated Champions League qualification, but that achievement has been followed by a disappointing campaign for the Magpies, who are eighth in the Premier League.
Newcastle failed to make it out of a tricky Champions League group as demands of playing in four competitions led to an injury-plagued campaign for Eddie Howe's side.
"Certainly there is a cautionary tale there that getting into Champions League also means greater demands," Postecoglou told reporters on Friday.
"Demands on players, demands on the squad and you have to be geared up for it or else it can affect all parts of your season.
"It has been tough on Newcastle this year because the progress last year was fantastic, the reward for that was Champions League and this year for whatever reason it has made it a really challenging season on all fronts for them."
Tottenham will be making their first return to St James' Park since last season's 6-1 hammering, which proved to be the nadir of a dismal campaign that led to Postecoglou's arrival from Celtic in the close-season.
The Australian did not watch that fixture back, but he did reflect on the importance of Tottenham's 4-1 victory over Newcastle in December.
Tottenham entered the match with a lengthy list of absentees and had lost four of their past five games.
"I think it was important in context of the results," Postecoglou said.
"I thought on that day we played really well. We were really aggressive and I thought our front-third play was probably the area that we got most joy out of on the day.
"From the results point of view it was important, but from a performance point of view no more so than any other game."
