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.

13. Tariq Lamptey - 6
So dangerous when he puts the burners on. Had Athens players backing off. A completely different option to have at right-back. At fault for Athens' third goal - he fell to the floor after a mismatch header when he should have tracked the runner Photo: Eva Gilbert Photography

14. Danny Welbeck - 6
Unlucky with rebound header, couldn't have done more to keep it on target as ball came quickly at him. Booked Photo: Eva Gilbert Photography

15. Simon Adingra - 7
All action display after this introduction. Couldn't direct a header on target from the back post. Superb shot from distance well saved. Gave ball away too cheaply Photo: Eva Gilbert Photography

16. Facundo Buonanotte - N/A
Worked hard but couldn’t impact the game Photo: Adam Hunger / Getty Images for Premier League