Liverpool will not win the league this season. For a week I let myself believe otherwise: beat Arsenal at Anfield on Sunday and the gap to the champions would be three points. Instead Kai Havertz scored after 16 minutes, Arsenal won 1-0, and the gap is nine. The squad is still short in a couple of areas, and those holes will not be fixed until the summer.

Alisson’s short pass out from the back went astray, Declan Rice drove a low ball across the box and Havertz finished at the far post. It was Arsenal’s first win at Anfield in 14 years.

Liverpool had the better of the rest of the first half. Florian Wirtz hit the underside of the bar with a free-kick. Alexis Mac Allister, unmarked, headed a Milos Kerkez cross over. When Alexander Isak went for a header in the box, Jurriën Timber pulled his shirt and nothing was given. Afterwards Andoni Iraola said he would tell Isak “next time he has to go to the floor”.

Mac Allister should have scored. Isak should have had the penalty. Fair play to Arsenal, though: it was a great defensive performance. They are the best defensive team in the league by far, and one of the best the Premier League has seen. They have conceded five goals in nine league games, and they had the league’s best defence last season too.

Liverpool’s attack had nowhere to go. Wirtz, Bradley Barcola, Cody Gakpo and Isak cost more than £350m between them in guaranteed fees. Arsenal gave them almost no space. But when you pay that kind of money, one of them has to produce something on a day like this. Wirtz very nearly did. Otherwise Liverpool did not trouble David Raya much, and they have now scored four league goals in five games at Anfield this season.

Start with left-back. Milos Kerkez is not good enough for Liverpool. He is not the reason they lost, and he whipped in the cross Mac Allister should have buried. He had plenty of the ball. But he is not good at defending, and too many simple passes went astray. He has had a season and a quarter since his £40m move. Liverpool need a replacement, and urgently.

A lot of people say Arsenal’s wide players don’t contribute enough goals and lack the star quality of other teams’ wingers. Noni Madueke, who started on the right, scored three league goals in Arsenal’s title-winning season. But there is one thing they do relentlessly. Every time a Liverpool winger had the chance to run at an Arsenal full-back, the Arsenal winger was either already there helping or pushing across to help.

Kerkez doesn’t even do that, and he’s a defender. The clearest example came as Madueke broke with the ball. Kerkez tripped, lost his balance and ended up on the floor. He got to his feet and jogged back. A defender, jogging back. If the alternative on the bench hadn’t been Kostas Tsimikas, he’d have been subbed there and then.

Midfield is the second hole. Trey Nyoni, making his first Premier League start, was good. When he went off just before the hour for Dominik Szoboszlai, the game went flat. Maybe it was coincidence. But Arsenal started winning cheap free-kicks, Liverpool played into their hands, and Arsenal do not need a second invitation. Nyoni has barely played, and Ryan Gravenberch, who was on the bench, is overrated. Liverpool are at least one midfielder short.

The bench made the same point. Tsimikas, who did eventually replace Kerkez late on, is not Liverpool standard. Lewis Koumas is full of running but not of the standard required to win league titles.

The case against me is obvious. It is 1 November and there are 29 league games left. Liverpool were the better side for long spells on Sunday, and with a penalty and a better header they would have drawn. Nine points does not end a season on its own.

My answer is that to close the gap, Liverpool would need to be close to perfect from here, and this side is not that. It is still a work in progress, still improving, and we will drop points along the way. Arsenal, with a defence that concedes barely once every other game, will not drop many.

Liverpool will finish in the top three when the season ends on 30 May 2027, and they will be back in the Champions League. Then they have to use the summer to fix full-back and midfield.

I thought we were going to win. I thought we were going to be in the title race. We aren’t. Not this year. Gutted.