Postecoglou has failed to secure a win in his first six games across all competitions, collecting only one point in both the Premier League and Europa League.
Under his management, Forest has dropped from seventh to 17th in the Premier League, now just one point above the relegation zone.
This winless streak marks an unwanted club record, making Postecoglou the first permanent manager in 100 years to not win any of his initial six matches.
Postecoglou acknowledged hearing the fans' displeasure and described the team's performance as “really disappointing”, shifting focus to their upcoming match against Newcastle.