Arsène Wenger laid bare the frustration after watching his Arsenal team come up short in the Europa League semi‑final against Atlético Madrid to miss out on the dream farewell to his job of 22 years.

Diego Costa – so often the scourge of Arsenal from his Chelsea days – scored the only goal of the second leg at the Estadio Metropolitano for a 2-1 Atlético triumph and they will face Marseille in the final in Lyon on 16 May.

Arsenal struggled to create clear chances against a supremely organised Atlético defence that has now kept 12 consecutive clean sheets at home and, amid the disappointment, Wenger also had to reflect upon the final avenue to Champions League qualification being shut down.

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It was Wenger’s 250th European game but there will not be another one for him at Arsenal. His final match before he leaves the club at the end of the season will be on Sunday week at Huddersfield Town’s John Smith’s Stadium. The manager is still to win a European trophy. “I am like the team – very sad and very disappointed,” Wenger said.

“I am even very frustrated, as well, because when you go out of a competition and you had the performances over the 180 minutes that we had, it is very difficult to take. For the club, there is now some time to think about what to do for next season.

“I think there are some good ingredients in our team and they will bounce back. These players have quality and, with the right additions in the summer, the team will compete next year.

“I have no plans at the moment. I have to recover first from a huge disappointment. I’m very, very sad to leave the club with that exit. I will take some time to recover from this. The game can be very cruel; sometimes it is very nice. But the suffering is very strong tonight.”

Arsenal’s task was made more difficult by the loss of the captain, Laurent Koscielny, in the early running to a ruptured achilles tendon. Koscielny has had problems with the achilles for some time. “It doesn’t look very good,” Wenger said. “You can always hope for a miracle on the scan but the first signs don’t look very good.”

Wenger’s regrets took in the first leg, when Arsenal dominated against an Atlético team that played with 10 men for 80 minutes. But they could score only once and they conceded a late goal to Antoine Griezmann.

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“The tie should be over in the first game,” Wenger said. “We were 1-0 up at home and we conceded a stupid goal. Then, tonight, we conceded on the counter with one minute to go before half-time. Those are vital moments in a game of this stature.

“Atlético played with a bit of fear in the first half but at 1-0 they had a bit of a cushion. Costa’s goal was vital. That’s why he is one of the best strikers in the world. We missed something in the final third. In the first half tonight, we had plenty of opportunities but we missed something always in the final ball. Even in the second-half, too.”

Wenger marvelled at Atlético’s defensive resilience, which was led by Diego Godín, but he complained about some cynical fouls from them. Gabi and Saúl Ñíguez were booked for stopping counter-attacks. “Gabi is happy to stay on the pitch,” Wenger said. “It took the referee a while to book Gabi. Those situations could have been very dangerous for us. But they are a clever side who defend very well.”