Greece is experiencing its worst year in the Champions League for 20 years after both of its representatives were knocked out before the group stage.
Olympiakos and PAOK were eliminated in the third qualifying round on Wednesday to end Greek involvement in Europe’s top club competition.
PAOK came close to completing a shock victory over Ajax but was unable to complete the task at the Toumba Stadium in Thessaloniki.
The Dutch former European champions came from behind to beat PAOK 2-1 and go through 3-2 on aggregate.
Stefanos Athanasiadis gave PAOK an early lead but captain Davy Klaassen levelled from the spot in first-half stoppage time before firing home an 88th-minute winner.
Meanwhile, it was a disappointing night for Greek champion Olympiakos in Israel, where the Reds lost 1-0 to Hapoel Beer-Sheva after a goalless first leg, Shir Tzedek scoring the decisive goal.
This was the first time since the 1996-7 season that a Greek side did not progress in the Champions League.
Olympiakos and PAOK will go into the draw for the Europa League play-offs on Friday. Panathinaikos, AEK and PAS Giannena, who are playing the second leg of their Europa League ties on Thursday night, will try to join them.