For Arsène Wenger, there will be no happy ending. “Rumbo hacia Lyon,” (road to Lyon) read the huge banner unfurled by the most boisterous section of Atlético Madrid supporters before this victory. Diego Simeone’s team are, as promised, on their way to the Europa League final and whatever tributes come for Wenger over the next 10 days – the promise of a statue, perhaps, or even a stand named in his honour at the Emirates – it will not be how he wanted the story to finish.

All that is left now is Sunday’s home game against Burnley, followed by the trips to Leicester and Huddersfield, and perhaps it is a fitting end to a season of drift. Arsenal came up short, as they often do against elite teams, and when they needed something special in the second half, losing to Diego Costa’s goal, they did not have the personnel to deliver it. Arsenal barely summoned a chance and the late onslaught that might have been anticipated never really materialised. There was only one goal in it – yet Arsenal were obliging opponents for a team with Atlético’s defensive expertise.

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This was Atlético’s 12th successive clean sheet at this stadium – an incredible run that goes back to 20 January and covers 1,097 minutes in play – and that parsimonious defending was the difference over the two legs. Atlético were brilliantly efficient at the back whereas it is more than 10 years since the same could be said of Wenger’s teams. He has never won a European trophy and, yes, it would have been a lovely way to go out after 22 years as Arsenal’s manager. Atlético, however, give the impression that fairytale endings are just that – for fairytales.

On top of everything else, Arsenal also lost Laurent Koscielny to a ruptured achilles tendon, an injury that will have ramifications for France. Koscielny, who has been nursing a long-standing problem, went down in such a way the seriousness of the injury immediately became apparent.

He pounded the turf in pain and frustration and his reaction was of a man who must have known straight away what it meant for his hopes of playing in the World Cup. Koscielny was supposed to retire after this summer’s tournament; instead, he will not be involved with Didier Deschamps’s team in Russia.

Quick guide Arsenal player ratings Show Hide David Ospina Did not spread confidence. Involved in a few mix-ups. Poor kicking. Saved from Torres late on. 6 Héctor Bellerín Caught on wrong side and out-muscled for Costa’s goal. Passed up promising situations on counter. 5 Shkodran Mustafi Much-maligned defender stood up to Costa. Made a host of important tackles and interceptions. 7 Laurent Koscielny Victim of early achilles horror, when he slipped and felt his leg buckle. Taken off on a stretcher. N/A Nacho Monreal Willing attacking outlet, pressed high, made runs. Struggled badly for end product. 5 Aaron Ramsey Chance in front of goal on 52 minutes – could not muster power. Worked to stretch Atlético. 6 Granit Xhaka Nobody on the field saw more of the ball. Generally sound with it. Went close with a long-range shot. 6 Jack Wilshere Tidy in possession, trademark quick feet, tried to drive the team. Walked off slowly when subbed. 6 Mesut Özil Looked smooth, as usual, but flicks did not always come off. Lacked killer touch. 5 Alexandre Lacazette In-form striker was suffocated. One flicker in area on 28 minutes but touch heavy. 5 Danny Welbeck Preferred to Mkhitaryan because of his work rate, he could not make anything happen. 5 Subsitutes: Calum Chambers (for Koscielny 12) 7, Henrikh Mkhitaryan (for Wilshere 68) 6 Ratings by David Hytner

Hypothetical now, but perhaps Arsenal might have coped better with Costa and Antoine Griezmann if their captain had lasted longer than seven minutes. Then again, Koscielny was badly at fault for Griezmann’s goal in the first leg. Griezmann had another fine game and when the two Atlético forwards combined at the end of the first half, in the time added on for Koscielny’s treatment, it led to the game’s decisive moment.

The goal showed the qualities of both players. Griezmann’s pass was beautifully weighted and once Costa had got behind Héctor Bellerín it was always going to be difficult for the Arsenal right-back to make up for his positional error. Bellerín might have been faster but Costa was stronger, shielding the ball with his body while expertly holding off his opponent. David Ospina, who had endured a nervous opening 45 minutes, advanced from his line and Costa swept the ball past Arsenal’s goalkeeper with a confident left-foot finish.

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Until the point the Arsenal supporters, positioned in the most vertiginous levels of this sweeping new-build stadium, must have been pleasantly surprised by the way their team had set about the game.

All the same, Wenger’s men had a lot of the ball without doing a great deal with it. Mesut Özil, for instance, was prominently involved without being able to pick out a killer pass. Atlético have conceded only 18 goals in 35 La Liga appearances this season and Arsenal needed more from their attacking players. Danny Welbeck and Alexandre Lacazette were disappointing.

In the second half Arsenal were attacking the end where their supporters were gathered and there were some encouraging moments early on. Granit Xhaka’s low shot brought the first noteworthy save from Jan Oblak and there were even a few moments of carelessness from the home team’s defenders.

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Bellerín’s surging runs from right-back were another feature and midway through the second half Wenger brought on Henrikh Mkhitaryan to increase his team’s attacking threat at the expense of Jack Wilshere.

Arsenal still found it difficult to get behind Atlético’s expertly organised defence. Mkhitaryan put one shot over the crossbar and the referee, Gianluca Rocchi, was too lenient on the sporadic occasions when Wenger’s team found themselves in encouraging positions and Simeone’s players – streetwise, to the end – gave away deliberate free-kicks.

Arsenal seemed to lose belief in the final exchanges and that, perhaps, was the most disappointing part. There was no burst of late pressure, no moving a defender into attack, no gambling – and, more than anything, no spark. The final whistle sounded and Wenger was quickly gone.