Olympiakos held by Alkmaar
The result left Olympiakos in second place in Group H with seven points, six behind already qualified Arsenal who will be their opponents in their final group match. Standard Liege are third on four points after losing 2-0 to Arsenal.
The Belgian side could pip Olympiakos to qualification if they win their final game at home to Alkmaar next month and Arsenal beat the Greeks at the Emirates Stadium.
In a lively first half the home side created more danger, though striker Jeremain Lens missed the target three times. Goalkeeper Sergio Romero made a good save to deny the Greek side's Jaouad Zairi.
Alkmaar, bottom of the group, wasted two more good opportunities to break the deadlock through Brett Holman and Pontus Wernbloom.
Brazilian Leonardo had the chance to score for Olympiakos minutes from the final whistle but Romero saved his shot.
Alkmaar coach Ronald Koeman was disappointed with his side for not scoring.
"Seeing this match there was only one team that deserved to win and that was us," Koeman told reporters. "(There were) not too many chances but we should have scored, while besides the opportunity for Zairi we gave away nothing."