The Lilywhites' underwhelming start to the 2024-25 season continued in front of the home crowd, where Gabriel Magalhaes's second-half header saw a depleted Arsenal side come away with all three points.
The Gunners travelled to the Tottenham Hotspur Stadium without two of their three first-choice midfielders in Declan Rice and Martin Odegaard, while Oleksandr Zinchenko, Riccardo Calafiori and Mikel Merino were also among the visitors' absentees.
In contrast, Tottenham had record signing Dominic Solanke and key centre-back Micky van de Ven back in their ranks for the derby, in which they dominated the possession and shot counter but were left to lament familiar mistakes.
After conceding twice from corners in this fixture last season, Spurs were exposed at set-pieces again for Gabriel's goal, while also showcasing a distinct lack of ruthlessness and creativity in the final third despite their offensive setup.
Postecoglou: 'I always win things in my second year'
Tottenham's loss to their long-time adversaries leaves them in the bottom half of the Premier League table with just four points from their first four matches of the season, and attention now turns to their midweek EFL Cup trip to Coventry City.
Spurs have not lifted a major trophy since triumphing in that tournament in the 2007-08 season, but Postecoglou arrived in North London with an extensive CV of winning silverware, having clinched 12 senior crowns throughout his managerial career.
Speaking to Sky Sports News after Sunday's loss, the 58-year-old remained bullish about Spurs' chances of lifting a trophy this season, affirming that he never fails to win silverware in his second year in a job.
Asked if he has seen enough from his Spurs side to suggest that they can conquer a competition this season, Postecoglou replied: "Can I answer the question or are you going to keep asking it?
"Absolutely. I'll correct myself, I don't usually win things, I always win things in my second year. Nothing has changed. I just said it now so I don't say things unless I believe them."
Does Postecoglou "always win" trophies in his second year?
Postecoglou only spent two years in the Celtic job before jumping ship for Tottenham, but true to his word, the Australian delivered a Scottish Premiership, Cup and League Cup treble to the Bhoys faithful in his second season.
The Spurs boss had already won a Scottish League Cup crown in his first year in the job, though, but his solitary Japanese top-flight title with Yokohama F Marinos did come in his second year in 2018-19.
Postecoglou's penchant for second-season success is not just limited to club football, as he also led Australia to an Asian Cup title two years after taking charge and guided Brisbane Roar to the 2010-11 Australian A-League title after joining in 2009.
In fact, the only senior job where Postecoglou has not won a major honour in his second season came with South Melbourne FC, whom he took charge of in 1995 and did not earn a trophy with until 1998.
There is otherwise more than enough evidence to back up the 59-year-old's claim, but if Sunday's dreary showing is anything to go by, his second-season streak will not hold up much longer.