Sean Dyche and his staff climbed the hill to the Acropolis ahead of the game and their team will now have to scale another major height to advance to the group stages of the Europa League after a controversial night in Athens.
The Clarets aren’t out of it and will still harbour hopes of turning this play-off tie around in what would be a famous second leg at Turf Moor next Thursday night.
An away goal – converted from the penalty spot by Chris Wood to make it 1-1 at half time – has kept alive hopes of a possible comeback as Burnley bravely saw out the last half hour with 10 men.
Ben Gibson's dismissal for a second yellow card came after the defender had been harshly penalised for conceding the penalty which allowed Olympiakos to take a two-goal aggregate lead on a night the 44-time Greek champions showed their quality.
But inside a hot, steamy and in-flamed George Karaiskakis Stadium, the Clarets displayed all their reserves of courage and commitment not to go under and leave the tie beyond them before they return to Lancashire to try and make home advantage count for the third time in their own Europa odyssey.
In the week the Clarets lost one of their favourite sons, it was appropriate Burnley were back on the big stage and following in the considerable footsteps of Jimmy McIlroy.
It was McIlroy’s league champions who first took Burnley into Europe in 1961, and while that side is rightly revered as arguably the Clarets’ best, the current line-up deserves great kudos for securing only a third European campaign in the club’s history thanks to their heroics in the Premier League last season.
And like McIlroy’s trail-blazers who went to the last eight of the European Cup, they are determined to make their mark as they chase a place in the group stages of their own competition.
They are having to do it the hard way though, with the draw throwing up now favours for Dyche’s men, who wore black arms bands in memory of their illustrious predecessor.
After over-coming Aberdeen and Istanbul Basaksehir in extra-time this was going up another level against a club that knows what European football is all about and, along with their febrile fans, clearly cherishes it.
After falling off their pedestal as Greek champions after seven successive title wins for the second time in their illustrious history last season, the Champions League is not an option this time around for Olympiakos.
But that has only increased their desire to go as far as possible in the Europa League and they made their intentions clear with a 7-1 demolition of Swiss side Lucerne in the previous round.
Manager Pedro Martins, brought in following the relative failure of last season’s third-place finish, kept the same starting line-up and saw his side take a 19th-minute lead.
Phil Bardsley’s foul on tricky winger Daniel Podence set up a free-kick chance which was delayed by a head injury to Jeff Hendrick.
That and a generous-looking 10-yard measurement to the defensive wall did little to help the Clarets organise and from 25 yards captain Kostas Fortounis struck a beauty past opposite number Tom Heaton, starting and leading the Clarets in a competitive game for the first time in almost 12 months.
If the Clarets were frustrated by the interpretation of referee Slavko Vincic on that occasion, they were grateful for the apparent clear-mindedness of the Slovenian around the half-hour as Burnley hit back to level with a potentially vital away goal.
Firstly, he turned down a penalty appeal from Podence after he had given Kevin Long the slip and gone down as the defender battled to retrieve the situation.
And then he did award the Clarets a spot-kick after Wood got himself between Mohamed Camara and the ball and was barged to the ground.
It was Ashley Barnes who had scored from the penalty spot to wrap up victory over Aberdeen a fortight ago. But facing a baying home crowd, Wood took the job on and kept his nerve to slot home the equaliser to reward the backing of the 1,000 Burnley fans at the other end of the ground.
Wood then headed a Johann Berg Gudmundsson corner just wide as the Clarets enjoyed their best spell and the Greeks went into the break even more frustrated after a cross from Fortounis driven against the hand of Ward, tucked behind his back, did not yield a penalty - despite massive protests from the home ranks who swarmed around the officials from on and off the pitch.
But a second Olympiakos goal was not far away and three minutes into a dramatic second half, the hosts went 2-1 up from another set-piece after Gibson had been penalised for a foul.
Fortounis this time didn’t go for goal, but picked out Andreas Bouchalakis who headed into the bottom corner as the Greeks, a real threat with their speed of movement and slick passing, then sensed the chance to take hold of the tie.
Heaton saved from Fortounis and with an hour gone the Clarets’ task was made even harder as Vincic again took centre stage.
Burnley must have feared the referee might not continue to stand firm and repel the pressure that was seemingly cranked up at the break, and when Camara shot into a crowded penalty area he penalised Gibson for handball as the defender looked to have blocked with his chest before the ball ricocheted onto his withdrawn lower arm.
To compound the situation, he then booked Gibson for the second time to end his night and leave the Clarets to try and keep their European hopes alive with 10 men once Fortounis had slotted home his second goal of the night.
James Tarkowski was sent on to replace Gibson with Wood sacrificed in attack, but with 17 minutes to go Olympiakos could have potentially put the tie to bed.
The outstanding Fortounis was again involved as the Greek international played in Miguel Angel Guerrero, who, fortunately for the Clarets, dragged his shot just wide.
But Burnley then stood firm and refused to buckle again and, with their supporters backing them to the end, made sure there would be no more than a two-goal deficit to try and wipe out in a week's time.
Burnley: Heaton, Bardsley, Long, Gibson, Ward (Lennon 66), Gudmundsson (Vokes 77), Cork, Hendrick, Taylor, Barnes, Wood (Tarkowski 62). Substitutes: Hart, Lowton, Westwood, Vydra.
Sent off: Gibson
Booked: Gudmundsson, Gibson, Long.
Olympiakos: Gianniotis, Elabdellaoui, Roderick, Vukovic, Tsimikas, Bouchalakis, Camara, Christodoulopoulos (Ansarifard 84), Fortounis (Fetfatzidis 88), Podence, Guerrero. Substitutes: Choutesiotis, Natcho, Vrousai, Torosidis, Cisse.
Booked: Christodoulopoulos, Bouchalakis
Referee: Slavko Vincic (Slovenia)