Ollie Watkins reduced the deficit for Unai Emery's side and Moussa Diaby equalised moments after the interval.

Olympiakos roared back in front with an El Kaabi penalty and a deflected strike from Santiago Hezze.

Douglas Luiz missed a late penalty, meaning Villa must overturn a two-goal deficit in the second leg in Piraeus on 9 May to reach their first European final since 1982.

"There were mistakes all round tonight and we'll take responsibility," McGinn told TNT Sports.

"We have a mountain to climb but we know we're capable. The manager was still positive in there. There's still a long way to go."

El Kaabi began the goal flurry with a clinical finish. It was initially disallowed for an offside, but that was overturned after a check by the video assistant referee (VAR).

The Morocco striker added a classy second when he latched on to Daniel Podence's clever pass over the top and slipped the ball under Robin Olsen.

Watkins pulled a goal back for Villa in added time in the first half with an angled finish from just outside the six-yard box.

Diaby then levelled as Konstantinos Tzolakis was beaten at his near post.

Villa seemed to have the momentum at that point but were sucker-punched by their visitors.

Douglas Luiz handled a Panagiotis Retsos header and El Kaabi coolly sent Olsen the wrong way from the resulting spot-kick to take his tally to eight goals in the competition.

There was more than an element of fortune to Olympiakos' fourth as Hezze's speculative effort flicked off the back of Ezri Konsa to wrong-foot Olsen.

Douglas Luiz had a late opportunity to atone for his error after David Carmo felled Jhon Duran but, to the incredulity of the home fans, he failed to hit the target.

Villa caught cold by bold Greeks

The presence of Villa fan Prince William, the Prince of Wales, and a colourful mosaic in the Holte End heightened a sense of expectation at a raucous Villa Park before kick-off.

Emery talked up the importance of a top-four Premier League finish in the build-up to this match, but for the fans in claret and blue it was dreams of a first major trophy since 1996 that largely occupied their thoughts.

If those dreams are to become a reality then Villa will need to be much improved in the second leg after they were caught cold by the intensity of an Olympiakos side motivated by their own sense of destiny.

The Greek Super League side have never reached a major European final and played with a fearless attacking verve as they pressed and harassed Villa into defensive lapses.

Certainly Villa's ability to play out from the back with composure was hampered by the absence of suspended goalkeeper Emiliano Martinez and ball-playing defender Pau Torres.

Emery cut an animated figure in the technical area as he tetchily issued instructions to his side, with both Olsen and Clement Lenglet facing his ire.

Villa may need a tactical masterclass from their Spanish manager if they are to have a chance of overhauling Jose Luis Mendilibar's side in Greece.

"We didn't play like we are playing and we need to keep being consistent," Emery told TNT Sports.

"They deserved to win and they are a good team. It's not about luck. We didn't play well. We have to play better."

In the other semi-final, M'Bala Nzola scored in added time as Fiorentina snatched a 3-2 home victory over a Club Bruges side who played nearly a third of the game with 10 men after Raphael Onyedika was sent off.

Riccardo Sottil had earlier put Fiorentina ahead before Hans Vanaken equalised from the penalty spot.

Andrea Belotti restored Fiorentina's advantage eight minutes before half-time, but Igor Thiago got the 10-man Belgian side back on level terms soon after the hour, before Nzola came up with the late winner.