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.
"Impossible," Postecoglou said during his pre-match interview when asked if there had been enough time to bed down his principles.
And after Saturday's result he admitted: "Disappointing with the outcome. It's not nice losing any game.
"They're a very good side and pretty formidable at home. But even in that context, it's disappointing."
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.
Arsenal dominated the first half, unleashing 11 shots to one and enjoying 60 per cent possession as they produced wave after wave of attacks.
Defender Morato looked particularly vulnerable as Arsenal targeted him time and again, with Noni Madueke starring.
Forest's defence looked 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 unleashed a wicked volley that took a slight deflection and slammed into the back of the net.
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 squared the ball to Gyökeres for an easy tap-in.
And it was game over in the 79th minute when Zubimendi headed home.
Elsewhere in the Premier League on Saturday Newcastle welcomed a new goalscoring hero following the departure of Alexander Isak as Nick Woltemade struck a debut winner in a 1-0 defeat of bottom side Wolves.
The German, signed from Stuttgart last month, headed home after 29 minutes at St James' Park, securing the Magpies' first win of the season and leaving Wolves still without a point.
An Antoine Semenyo penalty just after the hour proved decisive as Bournemouth beat Brighton 2-1 at the Vitality Stadium.
Gabriel Gudmundsson headed into his own net as Fulham snatched a last-gasp 1-0 win over Leeds at Craven Cottage.
The Everton v Aston Villa and Crystal Palace v Sunderland fixtures finished 0-0.
And Postecoglou's former side Tottenham ran out comfortable 3-0 winners over 10-man West Ham in the first of the evening matches.
Pape Matar Sarr, Lucas Bergvall and Micky van de Ven were on target against the struggling Hammers, who had Tomas Soucek sent off.
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