1-0 north London derby defeat by Arsenal.
Gabriel scored the only goal at Tottenham Hotspur Stadium with a header from a corner to send the Gunners into second spot.
Spurs, though, have only won one of their four Premier League games this term.
Former Celtic boss Postecoglou is in his second season at the club, having led them to fifth place in 2023-24.
After the disappointing loss, the Australian was asked about a pre-season interview where he said "usually in my second season I win things".
He told Sky Sports: "I'll correct myself - I don't usually win things, I always win things in my second year.