Where do Arsenal go from here? It is easier to say where their travels will not be taking them. They will be confined to England for at least the next year, any realistic hope of European football in 2021-22 having been put beyond them by an astute Villarreal side that held them at arm’s length to deservedly reach the Europa League final. The blunt truth, on a night when they were required to stand tall, was that Mikel Arteta’s players showed neither the backbone nor the cohesion to fare any better. What an embarrassment it is for a club that felt affronted when, after 17 successive seasons in the Champions League, they dropped into the continent’s second-tier competition four years ago. Barring an extraordinary set of outcomes in the Premier League’s final fortnight they will be confined to the domestic game for the first time since 1996 and it is hard to feel sorry for the chief architects of such an ungraceful decline. The Kroenke family may believe Arsenal belong in an elite, anti-competitive closed shop but, back in the real world, the diminishment has occurred on their watch. They would do well to expend energy on some vigorous soul searching closer to home rather than attempting to cheat an existing football structure that their asset currently appears a million miles from mastering. It is a significant personal setback, too, for Arteta. He was outdone over two legs by Unai Emery, the manager who was removed before his appointment, and only one of these teams ever seemed sure of their jobs. Arteta had overcomplicated his first-leg selection and went for broke here with an attack-minded lineup that, on paper, promised to fizz with creativity and movement. Instead they produced the dampest of squibs and there was the nagging sense, watching his players struggle to form the combinations that might break down relatively modest opponents, that he is approaching the confused, flailing territory that eventually accounted for his predecessor. Arteta’s job is not yet in danger but he will begin next season running dangerously low on the credit he amassed upon taking over. He sounded husky after the match, voice and nerves stretched to the maximum by 95 sometimes frenetic minutes of huff and puff. Arsenal had, he said, shown “enthusiasm and desire” to reach the final but they must have kept it well hidden: nobody seized the moment and it meant that for long spells Villarreal could pass the time untroubled. There was, as is customary, a standout moment of regret. When Pierre-Emerick Aubameyang rose to meet Héctor Bellerín’s delivery 11 minutes from time he seemed to have done it yet again: lifting Arsenal above the mediocre and potentially, on this occasion, setting a path back to the elite. But his header struck the inside of Gerónimo Rulli’s right post, bounced out and was spirited away from goal; Arsenal came no closer and rarely raised the tempo to a level that might turn the screw. Aubameyang had already glanced the woodwork once, striking an angled volley against the outside of an upright in Arsenal’s only real first-half chance. Arteta had surrounded his captain with Nicolas Pépé, Bukayo Saka, Emile Smith Rowe and Martin Ødegaard, in effect leaving Thomas Partey to man the midfield. Partey was desperately sub-par in the event and when he inadvertently tested Bernd Leno early on with a wayward back pass, it symbolised the home side’s lack of control. Emery had set Villarreal up in a steady, functional 4-3-3 that occasionally sparkled when Samuel Chukwueze took possession on the right. He drew an early save from Leno but was forced off though injury on the half-hour. The La Liga team’s attacking threat largely subsided from there; they operated with caution and it was no huge exaggeration to say the primary danger to their progress came from Rulli, who was fortunate nobody pounced when he fumbled an Aubameyang shot before half-time and saw Smith Rowe float a good opportunity off target early in the second half after he had floundered under a cross. It was clear Arsenal should have tested Rulli more. Arteta could point to the fact Alexandre Lacazette was only fit for a 10-minute cameo while perhaps their left side would have offered greater vigour if Kieran Tierney, pressed into action after Granit Xhaka’s warm-up injury, had been fully match-ready. He will find it hard, though, to make excuses wash. Two years ago Emery led Arsenal to a convincing semi-final win over Valencia, naming a team that included five players Arteta subsequently did not want. This time, coincidentally fielding the same central midfield of Dani Parejo and Francis Coquelin that had floundered against Arsenal that day, he beat them with a side that looked greater than the sum of its parts. The managers’ understated handshake at the end said nothing of such a sharp narrative twist, but there will be plenty to hear about Arsenal’s seemingly irreversible atrophy over the coming months.