Prince William was among the Villa fans left disappointed in the stands as a bad night for Emery’s men capped a miserable season for English clubs in Europe.
Villa are the sole survivors from the Premier League at the semi-final stage of the three European competitions.
“Everything that could go wrong did go wrong tonight,” said Villa captain John McGinn.
“Just mistakes all round tonight. We take responsibility but it is up to us to go to Greece next week and turn it around because we are more than capable.”
Olympiakos showed no signs of nerves in their first ever European semi-final with El Kaabi taking his tally for the season to 30 goals.
The Moroccan striker was initially flagged offside for the opener on 17 minutes but a VAR check showed he had timed his run perfectly to slot in from Chiquinho’s flick.
Villa are set for even more glamorous European nights next season as they sit fourth in the Premier League and within touching distance of securing Champions League football.
However, signs of fatigue have shown in recent weeks at the end of a gruelling campaign and they were cut open easily once more for Olympiakos’ second.
El Kaabi sprung the offside trap again to round Robin Olsen and double the visitors’ lead.
Momentum looked to have swung back in favour of the hosts either side of half-time.
Ollie Watkins reduced the deficit with his 27th goal of the season in first-half stoppage time before Moussa Diaby levelled when he caught out Konstantinos Tzolakis at his near post
Yet, Villa were only level for four minutes as Douglas Luiz needlessly raised his arm to block at an Olympiakos corner.
Emery insisted on the eve of the game that he had full faith in understudy goalkeeper Olsen, but Villa badly missed the presence of the suspended Emi Martinez, whose penalty heroics had won a tense quarter-final against Lille.
El Kaabi coolly sent Olsen the wrong way from the spot to complete his hat-trick.
The Swedish stopper was then wrong-footed when Santiago Hezze’s strike deflected off Ezri Konsa.
Luiz had the chance to atone for his earlier error and set up a grandstand finish when Villa were awarded a penalty six minutes from time.
But the Brazilian’s effort hit the post to leave Emery needing to produce a miracle in Piraeus next week to add another European trophy to his CV.
© Agence France-Presse
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