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.

1. Joao Pedro scored a brace for Brighton
Joao Pedro scored twice from the penalty spot but Albion lost 3-2 against AEK Athens in the Europa League (Photo by Mike Hewitt/Getty Images) Photo: Mike Hewitt/Getty Images

2. Jason Steele - 6
No chance of saving the powerful header that opened the scoring. Crucial save at 1-0 from Garcia, who was one-on-one. Can't be blamed for the second goal. Did his best to stop the third goal to no avail. Otherwise, he wasn't troubled a great deal. Photo: Eva Gilbert Photography

3. James Milner - 6
First player to play for five different English clubs in major European competitions. Got forward well in early stages and found himself in front of goal but couldn't find a shot and pass was blocked. Some good defending against quick forwards. Photo: Eva Gilbert Photography

4. Jan van Hecke - 6
Clumsy foul which resulted in Brighton conceding the second goal. The Dutchman tried to get a foot on the cross but beaten to it. Made a vital sliding challenge at the end of the first half. Improved after the break and looked more composed. Booked Photo: Alex Pantling / Getty Images