Postecoglou was sacked by Tottenham in June, but he was back in the EPL hot seat on Saturday against a rampant Arsenal outfit who showed why they are one of the favourites for this season's title.
Arsenal midfielder Martin Zubimendi scored a double - including an audacious 22-yard volley - and Viktor Gyökeres enjoyed an easy tap-in during the rout.
Postecoglou had just days to get his squad ready for the match following the controversial sacking of Portuguese boss Nuno Espirito Santo, who fell out with Forest owner Evangelos Marinakis.
It meant Postecoglou didn't have enough time to implement his famed Ange-ball: an attacking and high-intensity football style.
"Impossible," Postecoglou said during his pre-match interview when asked if there had been enough time to bed down his principles.
Arsenal unleashed 16 shots to five for the match, and they could have easily scored more goals against a shaky Forest defence.
Arsenal fans were quick to remind Postecoglou of the cut-throat nature of the EPL, chanting: "You're going to get sacked in the morning" midway through the second half.
Then shortly after Forest conceded their third goal in the 79th minute, Arsenal fans taunted Postecoglou again by singing: "Are you Tottenham in disguise?"
Forest are now one win, one draw and two losses after four league games, with Postecoglou facing a big task to get his players up to speed over the coming weeks and months.
Postecoglou was dealt a huge blow when star Nigerian defender Ola Aina was ruled out for three months due to a hamstring tear he suffered while on international duty.
Brazilian Morato came into the side against Arsenal in the only change Postecoglou made to the XI from the recent 3-0 loss to Aston Villa.
Arsenal dominated the first half, unleashing 11 shots to one and enjoying 60 per cent possession as they produced wave after wave of attacks.
Morato looked particularly vulnerable as Arsenal targeted him time and again, with Noni Madueke starring.
Mikel Merino had a great chance to open the scoring in the seventh minute with a close-range strike, but Forest goalkeeper Matz Sels did well to block the shot.
Forest's defence continued to look shaky, but it took a wonder strike from Zubimendi in the 32nd minute to finally break them.
A defensive header from a corner looped to Zubimendi, and the Spaniard didn't even let it bounce as he unleashed a wicked volley that took a slight deflection and slammed into the back of the net.
Forest's finest moments of the first half came late, with the best chance falling to Morgan Gibbs-White, who shot wide under pressure after combining with Chris Wood for a swift one-two pass.
Postecoglou's half-time pep talk came to nothing as Arsenal made it 2-0 just 46 seconds into the second half when Eberechi Eze made the most of a defensive error to get in behind and square the ball to Gyökeres for an easy tap-in.
And it was game over in the 79th minute when Zubimendi headed home.
Forest's closest moment came in the 52nd minute when Wood used his chest to deflect a teammate's bullet pass, with the ball floating over the goalkeeper and bouncing off the crossbar.
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