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.
9. Ansu Fati - 5
Largely quiet game for the Barcelona loanee. Took up a playmaker role, linking up with Mitoma and Estupinan. One clumsy pass straight to Athens player. Had a good shot well saved in the second half. Excellent siding tackle to win the ball back start an attack. Needed to take a bit more time when given the ball. Missed chance to shoot after great pass by March Photo: Eva Gilbert Photography
10. Kaoru Mitoma - 6
Good pressing from the front. Superb skill to beat his man but cross too close to the keeper. Limited impact in the second half and was replaced late on Photo: Eva Gilbert Photography
11. Solly March - 6
Great to see him back from injury. Superb pass through to Milner for game's first real chance. Bucket loads of space out wide but unable to find a killer ball. Sometimes he could have pulled the trigger a bit quicker. Good interception. Did really well to beat his man and find Fati in front of goal in injury-time. Tame right footed shot from distance Photo: Mike Hewitt / Getty Images
12. João Pedro - 8
Scored Brighton's first ever European goals with two coolly taken penalties which he won himself. Showed such composure in pressurised situations. Wrong booked for diving for the first one initially but VAR came to the rescue. Fouled again by same man and made no mistake from the spot once more. A hard working display and linked up nicely with his teammates. Was guilty of trying to be too clever and losing the ball once or twice. Should have squared to Mitoma when through on goal. Photo: Mike Hewitt / Getty Images