Arsenal's Europa League hopes were dashed as Villarreal sealed a semi-final victory that will almost certainly end the Gunners' unbroken 25-season run of appearing in European competition.
Trailing 2-1 from the first leg in Spain and knowing that victory in this tournament represented their only realistic route back into the Champions League, Mikel Arteta's side could not find a way past the visitors' steadfast defensive lineup.
Pierre-Emerick Aubameyang struck the post with a volley but it was a rare moment of threat in a display strangely passive for large parts.
Nicolas Pepe and Emile Smith Rowe both fired efforts wide early in the second half and Aubameyang hit the post again with a downward header later in the game, but such moments were few and far between.
That the defeat came at the hands of former boss Unai Emery will be especially disappointing for the Gunners. Emery was sacked in November 2019 after 18 months in charge, ultimately leading to the appointment of Arteta.
With Manchester United seeing off Roma in the other semi-final and Chelsea and Manchester City into the Champions League final, Arsenal's loss ruins hopes of a Premier League clean sweep of European competitions this season.
Villarreal will face United in Gdansk's Stadion Miejski on 26 May.
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