The world moves on. Technology develops and evolves. The aesthetics of the spectacle, perhaps, to our wearily nostalgic culture, have less to recommend them than they did, but accuracy at least is guaranteed. Where once epoch-defining line decisions were taken by Azerbaijani men with silver hair and splendid moustaches, now we watch a digital representation of a yellow circle landing on a white line across a green background. What Tofiq Bahramov’s decisive nod was to the 1966 World Cup, so the Goal Decision System may be to the 2018‑19 Premier League.

Where the former remains contested (with good reason), there is no disputing what happened at the Etihad on Thursday. Or at least not beyond crazed conspiracists who within hours of the final whistle were already talking about shadows and angles and the grand anti-Liverpudlian plot that is geometry. Perhaps the technology is not perfect. Perhaps the reading that said the ball was 11.7 millimetres from completely crossing the line is affecting an impossible level of accuracy, but it is still much more likely to be right than a 41-year‑old former footballer from Baku.

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11.7mm. It is the length of a bluebottle, the thickness of a pocket diary, the width of the nail on a little finger. It is nothing on which to lose a football match, still less perhaps a championship. There is a danger now that the measurement comes to haunt Liverpool as surely as Steven Gerrard’s “This does not slip” speech after another game against Manchester City; that when the history of this long title drought is written, the measurement 11.7mm looms so large that every time Liverpool fans see a fly, check an appointment or catch a glimpse of their own hands they are reminded of defeat and failure.

But Liverpool are still four points clear, a fact Jürgen Klopp was understandably keen to emphasise, and the tightness of the margins perhaps serve as a useful reminder that football, even at the highest level, is often chaos. However much you plan and organise, there are certain games that are decided, depending how much agency you wish to credit players with, on the whims of fate or by tiny details in the moment. Sadio Mané’s shot hit the post and bounced out; Leroy Sané’s was a fraction nearer the centre of the goal and so hit the post and cannoned in. This was a game won not in the macro but in the micro.

Facebook Twitter Pinterest The Goal Decision System showed the ball failed to cross the line by just 11.7 millimetres Photograph: Sky Sports

That 11.7mm could have a huge impact. It may be that Liverpool can brush off the disappointment. It may be that the sting of defeat elevates them to yet greater heights. But there is a danger that when that 11.7mm is added to the accumulated history of the past 29 years, the pressure becomes intolerable, that the hope and anxiety and hysteria become too much. This is a test, more than anything, of Klopp as a psychologist and a motivator. Looked at coldly, beyond the result, the signs on Thursday for Liverpool were good.

Again, they unsettled City with their pace and menace on the counter. Again, City looked uncomfortable when pressed hard, their pass completion rate was down to 80.8% against a season average of 88.7%. This has become a recurring theme of late. Southampton unnerved City in a similar way last weekend. In slightly different ways, Leicester and Crystal Palace have shown City can be got at. It is a risk: play aggressively against them and you might end up being thrashed as City exploit the space that will inevitably be left behind the midfield (just as Sané’s winner came from a rapid transition) but there is a vulnerability there that can be exploited.

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The one tactical frustration for Liverpool, perhaps, would be how lacking in inspiration their midfield three looked early in the second half once they had to chase the game – and it is probably significant that the three of Jordan Henderson, James Milner and Georginio Wijnaldum had looked equally unimaginative in the second half of the defeat away to Paris Saint-Germain.

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The shift to a 4-2-3-1 opened the game up, in part perhaps because Fernandinho suddenly had a direct opponent in Roberto Firmino, but also because Mohamed Salah moved more centrally, away from the flank where Aymeric Laporte, a conservative selection at left-back from Pep Guardiola, had done a fine job of marshalling him. Again the lesson is clear for teams playing City: if they are prepared to risk humiliation, pushing a forward high against Fernandinho disrupts City’s rhythm.

City are not the relentless machine of the autumn. They look more human now, more fragile. Yet the gap is down to four points and the sense is that momentum is with them. The lead, though, is still with Liverpool thanks to their extraordinary December. All else being equal a four-point lead should still be decisive but, as Sir Alex Ferguson would always say, what matters most is less a defeat than the reaction to it.

Defeats happen, even to the best sides, even by the finest margins. What Klopp has to do now is ensure that 11.7mm does not become a millstone, an eternal measure on Merseyside of the gap between aspiration and actuality.