Joao Pedro scored twice from the penalty spot – levelling the score on both occasions – after Albion were undone by two set pieces.
There was a large Lewis Dunk shaped hole in the defence, with the captain missing out through injury.
For the first goal, no one was marking Djibril Sidibe on the edge of the box but it was a simply superb header and great spot from the corner taker.
Brighton were creating chances but Athens looked dangerous, with two big opportunities to make it 2-0. Brighton built up some momentum and were awarded a penalty, thanks to VAR, when Joao Pedro was tripped in the box.
The Brazilian forward stepped up and sent the keeper the wrong way to score Albion's first ever European goal.
But Athens were soon back in front after another set piece was turned in by Mijat Gacinovic. Dunk's absence was being felt – both his leadership and prowess at the back.
There was a long stoppage for an injury to Athens player Ehsan Hajsafi at the beginning of the second half, resulting in 13 minutes being added on at the end of the game.
Albion won another penalty when Pedro was once again clearly fouled by Damian Szymanski but it needed a VAR check once more. Pedro completed the sequence of déjà vu, as he stepped up and, despite being made to wait a long time, made no mistake with another calm penalty.
Athens took the lead for the third time in the game, and it was another poor goal to concede, as a long ball over the top left the defenders in disarray and Ezequiel Ponce squeezed the ball past a helpless Jason Steele.
Albion searched for a third equaliser but ultimately fell short as their European debut ended in an anti-climax.
5. Igor Julio - 5
Should have made it a dream debut with a goal but somehow missed the target with close range effort. Booked in second-half. Guilty of being slow to react to a couple of situations. Just lacking that commanding presence of Dunk. Needs time to adjust to the new team. Photo: Mike Hewitt / Getty Images
6. Pervis Estupinan - 6
Bursting run forward in the opening minute and somehow not awarded a free kick after being pushed over. A dangerous cross caused panic in the box. Linked up nicely with Mitoma. Booked. A couple of sloppy passes Photo: Eva Gilbert Photography
7. Pascal Groß - 6
Took captain's armband in Dunk's absence. Seen giving out orders in the midfield. A couple of misplaced pass out wide early and didn’t look his usual self. Lacked killer ball in forward areas this evening. Powerful shot saved Photo: Eva Gilbert Photography
8. Billy Gilmour - 7
Player of the match in the first half. Did well to keep hold of possession in pressurised situations. Was pulling the strings, with some lovely passing. One particular through ball played Ansu Fati in on goal. The Scotsman is a silky player and so good to watch. Some poor passes crept into his game in the second half. Photo: Mike Hewitt / Getty Images