Nottingham Forest felt aggrieved at a number of decisions in their recent defeat against Everton while Chelsea had a stoppage-time winner ruled out in their 2-2 draw against Aston Villa.
Postecoglou, whose fifth-placed team travel to Chelsea on Thursday, said he felt his team should have had a spot-kick during their 3-2 defeat by leaders Arsenal at the weekend.
"I thought we should have had a penalty on the weekend, other people didn't think we should have had a penalty on the weekend," he said.
"I wasn't sure about Micky van de Ven's offside but other people say it is offside. At the end of the day, who am I to sit in a room and tell officials how to do their job? They should know that - that is their job."
The Australian said VAR was here to stay despite misgivings over the technology.
"I'd change a hell of a lot on it but again I've said before that I think it's changed the game materially, which I don't think was the intention when it was brought in," he said.
Postecoglou joked that he would move to Sweden to get away from VAR.
"Yeah, I'm moving there," he said. "I don't have a job, I'm just moving there."
The Spurs boss said his team, who still have a chance of qualifying for next season's Champions League, were showing clear signs of progress despite the damaging defeat to Arsenal, which left them seven points behind fourth-placed Aston Villa, albeit with two games in hand.
"Absolutely yeah, absolutely," he said. "Clearly, clearly. As clear as you want it to be, 20-20, definitely, 100 per cent.
"We're playing our football, measuring ourselves against the best. The players have got a real belief in what we're doing. That's all I need to see."
Tottenham will be without Ben Davies, who has a calf injury, and Timo Werner, who has hurt his hamstring, for the trip to Stamford Bridge.
Both sustained injuries during the Arsenal defeat and will not play again this season, which could prove to be Werner's final appearance, although Spurs do have the option to turn his loan from RB Leipzig into a permanent deal.
