Inevitability is a dangerous sensation in football. Nothing is ever certain. No matter how great the general sense of domination, no matter how impressive the possession stats, at some point a team still has to ­actually put the ball in the net.

For a long time on Saturday here the feeling was that Arsenal would score at some point. They had to. They had all the ball. There were enough chances and half-chances to maintain the general feeling that a breakthrough would come. But it did not – and so, with Liverpool dropping points, another opportunity to close the gap at the top was missed.

Related: Liverpool 2-2 Fulham, Arsenal 0-0 Everton: Premier League clockwatch – live reaction

“When you do what we did today you have to win the game,” said Mikel Arteta . “I’m very disappointed not to win. We gave nothing away. If there was one team [that] deserved to win it was Arsenal. But at the end, you need a spark and you have to be precise.”

Both those qualities were lacking and, for the second week in a row, Arsenal were short of ideas against a side who sat deep and defended in numbers – even if they might have been awarded a penalty for Vitalii Mykolenko’s lunge on Thomas Partey. Three and a half league games have gone by since they scored from open play. It is one thing to make a virtue of set pieces, quite another for that to become the only means of attack.

There were opportunities. Twice early on Martin Ødegaard missed the target from decent positions and then saw an effort deflected over by James Tarkowski and Jordan Pickford. Pickford kicked away a Gabriel Martinelli effort just before half-time and then, early in the second half, got down well to save a Saka volley. Had any of those gone in, this probably would have been a comfortable win.

But they did not and, slowly, the grumbles of frustration snowballed and Arsenal’s reserves of inspiration dribbled away. There were a lot of crosses, but few of them good. It was all very Fulham last week: Arsenal controlling the ball without really driving home their advantage. Ødegaard, whose return from injury has been so key to the recent upturn in Arsenal’s form, was withdrawn on the hour having, despite those early opportunities, not reached the heights of which he is capable.

The threat Everton posed was extremely limited, but it hardly mattered. “It’s highly unlikely you’re going to come to places like this and dominate the ball,” said Sean Dyche. “So what’s important is what you do without it. Our focus and attention to detail were excellent.”

Abdoulaye Doucouré had their only chance of note but, set through by Orel Mangala, dawdled to allow Gabriel to get back and make a block. But their priority was less in scoring than in thwarting Arsenal which they did with relative ease, in part by their organisation and resilience, in part through the excellence of Pickford and in part through time-wasting, for which they collected two yellow cards.

Increasingly with Arsenal there is a sense of the game being a diverting imposition between the real business of the corners. Perhaps they are necessary context-setting longueurs, just as even the most schlocky of thrillers needs its exposition between the shootouts and car chases. But still, the set plays are the bits everybody wants to see. Of all the sides in the modern Premier League, though, the one least likely to be troubled by balls into the box is Everton. Dyche lives for set plays (although he leaves specific preparation to his assistants Ian Woan and Steve Stone – “Woany and Stoney”); it’s almost an insult to his professional pride to think you can beat his side by dead balls alone.

It was not until the fourth of the five corners Arsenal had in the first half that they troubled Everton, but Pickford, backpedalling, was able to tip the ball away. Mikel Merino did get to the first corner of the second half, an inswinger from Saka, but his header was straight at Pickford. How do you deal with Arsenal’s dead-ball threat? How do you defang Nicolas Jover, their great auteur of the dead ball? Having two massive centre-backs as good in the air as Tarkowski and Jarrad Branthwaite really helps.

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Of late, if you can blunt Arsenal’s set-piece threat, you are a long way to stifling them more generally. Everton’s fourth 0-0 draw of the season eases the pressure on Dyche. Arsenal are still just about in the title race, but their margin of error for the rest of the season is narrowing rapidly.