It was, as everybody pointed out, inevitable that the north London derby would be decided by a set play, Gabriel heading the only goal in the second half as Tottenham in general, and Cristian Romero in particular, switched off. It was a win that kept Arsenal within touching distance of Manchester City – and that it’s not absurd to think in such terms even at this early stage of the season suggests just how City’s relentless excellence has affected the perspective – but it also raised further doubts about Ange Postecoglou.

The heady start to last season, in which Spurs took 26 points from their first 10 games under the Australian, feels a long time ago. It was inevitable there would be some sort of regression to the mean but 44 points from their subsequent 32 games is a poor enough record to raise concerns. Extrapolate that over a season and you get 52, which is what West Ham got last season in finishing ninth. For Tottenham, with their expenditure and their stadium, that would be far from acceptable. Cherrypicking isolated parts of a season is never entirely fair, but 32 games is a hefty sample size.

“For some reason people think I don’t care about set pieces and it’s a narrative that you can keep going on for ages and ages,” Postecoglou said on Sunday. “I understand that. We work on them all the time like we do for every other team. You know that they’re a threat, as I said, for the most part, we handled them really well today, but we switched off for one and we paid a price and you learn from that and you move on.”

There was an obvious grumpiness there, which is perhaps only to be expected, but the “for some reason” seemed needlessly passive aggressive. The reason is that Postecoglou dug himself a hole last season, saying of working specifically on set pieces, “I’m just not interested in it. I never have been.” He did clarify that to explain that, on a philosophical level, he prefers to see the game holistically rather than hiving off one aspect to a specialist set-piece coach, as Arsenal have done with Nicolas Jover.

“It’s something that we work on along with everything in our game,” he said in May. “There are far more important things that we need to concentrate on at the moment in terms of the team we’re building.” Assistant coach Nick Montgomery was brought in during the summer and while he is not a specific set-piece coach, he does appear to have responsibility for them. But then if Tottenham let teams crowd Guglielmo Vicario as Arsenal did, and if Romero is so easily brushed aside by opponents, the problem soon becomes less about structures than about individuals.

Which may be true, but as a proportion of total goals conceded only Nottingham Forest let in more from set pieces than Tottenham last season – and the Premier League is ruthless; no weakness goes unexploited. Gabriel’s goal was the first that Spurs have conceded from a set play so far this campaign, but another pattern, just as damaging, is emerging. In all four games so far this season, they have had at least 60% possession, yet they have won only won one of them. In all four they have been ostensibly the better team – although Newcastle did ultimately register the better xG – but they have not created the chances they probably should have, have not, other than against Everton, taken their chances, and then have had their soft underbelly exposed.

Postecoglou sides tend to be at their best in his second season in charge: he himself made reference to that on Sunday, correcting a journalist who had said Postecoglou “normally” wins a trophy in his second season to insist he “always” does – and it did happen with South Melbourne, Brisbane Roar, Yokohama F Marinos and Celtic; at the last three of those that trophy was the league. Even if City are handed an enormous points deduction, it seems hard to imagine that happening this season.

Yet what must be frustrating for Postecoglou is that his side don’t seem that far off. It sounds vaguely ludicrous to say of a team on four points but it really wouldn’t have taken too much to go differently for them to have won four out of four at the start of this season. In the expected points world, Tottenham are just one point behind Arsenal. But back in the real, actual world they’re already six points behind their rivals and four points off the Champions League spots. The basic processes seem there: they just need a little more ruthlessness, a little less carelessness, a little more confidence and decisiveness. The problem is that Tottenham, of all clubs, have heard this before: that is the very essence of Spursiness.

At the beginning of last season, it seemed as though Postecoglou’s uncomplicated gruffness might be just the thing to cut through the years of underachievement. The problem now is that, as manifested in the problem of set-piece defending, it may have become a contributory factor.

• This is an extract from Soccer with Jonathan Wilson, a weekly look from the Guardian US at the game in Europe and beyond. Subscribe for free here. Have a question for Jonathan? Email soccerwithjw@theguardian.com, and he’ll answer the best in a future edition