The hosts were 2-1 winners in Spain, taking the lead early through Manu Trigueros before Raul Albiol doubled the La Liga side’s advantage on the half-hour mark.
Nicolas Pepe pulled one back for Arsenal from the penalty spot in the second half, after team-mate Dani Ceballos was sent off and before ex-Spurs man Etienne Capoue was shown a red card for Villarreal.
“It’s clear that we’ve won and it’s a good result, but seeing how the game went we should have killed them.
“I can’t explain what’s happened [in the second half]. We’ve had clear chances, they’ve found a penalty that I haven’t seen.”
In the Villarreal dugout was former Arsenal coach Unai Emery, Mikel Arteta’s predecessor in north London.
In the evening’s other semi-final first leg, Manchester United were 6-2 victors at home to Roma.
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