Instead, the frustration goes on for the 60-year-old Australian boss after his first match at his new City Ground home in Nottingham ended with Forest succumbing 1-0 to Sunderland in another Premier League match they really ought to have won.
Omar Alderete's first-half header helped Sunderland clinch their first away win of the season and consigned Postecoglou to a fifth match without a win since he took charge, leaving Forest in 16th place on just five points.
Postecoglou's crew haven't won since the opening day when Nuno Espirito Santo was still in charge.
The fans, the vast majority of whom had never wanted Nuno to leave after he had taken them into Europe, still need to be convinced by their new custodian and many will doubtless have looked on with a touch of regret on Saturday as West Ham, having sacked Graham Potter, announced the Portuguese as their new boss.
The match turned on a contentious first-half moment when referee Tony Harrington awarded Sunderland a free-kick in a dangerous area and booked Forest's Argentine midfielder Nicolas Dominguez for diving when he was trying to clear the ball while challenging with Trai Hume.
From the resulting free-kick, Granit Xhaka's neatly taken delivery enabled Paraguay international Alderete to ghost in at the back post and nod home his maiden goal for the club.
Forest were poor in the opening half, without a shot on target, but they dominated after the break, as Sunderland goalkeeper Robin Roefs made six saves to ensure they pickpocketed the points.
There was clear agony for Postecoglou who at one point fell to his knees in dismay after watching his unmarked New Zealand international striker Chris Wood missing a header from close range.
"We are in a cycle at the moment where we are getting every outcome out of the game except the win, and that is the most important thing," sighed Postecoglou.
"It was one of those evenings where we should have got the outcome we wanted.
"We had enough chances to win the game. We conceded a really poor goal - albeit from a poor decision from the official - but after that, we had enough chances to win the game."
There were boos from some Forest fans at the end, but they may have been aimed at officials as much as the team,.
"We have the foundation to win games of football but we are not and we need to change that," said Postecoglou.
"Fans have got every right to be disappointed, they want to see their team win.
"I understand their disappointment, it's certainly shared by us in the dressing room and by me, and my job is to rectify that."
Postecoglou's next chance to break his duck will come in the Europa League clash at home to Danish side Midtjylland on Thursday, before Forest have a difficult visit to Newcastle in the league next Sunday.
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