Ronald Koeman's side needed a win to keep alive any hope of progressing from Group H after taking just two points from their opening four games.

But they were unable to find a way past visiting keeper Antonis Nikopolidis as Olympiacos moved three points clear of third-placed Standard Liege with one game remaining.

After a scrappy opening spell, Leonardo drew a routine first save of the match from home keeper Sergio Romero.

Gill Swerts and Stijn Schaars each shot wide for the hosts either side of Dudu's effort for Olympiacos, which cleared Romero's crossbar.

Jaouad Zairi was also off target for the Greek side before AZ's Jeremain Lens twice fired wide from around 12 yards.

Romero blocked Kostas Mitroglou's effort before Lens wasted the best chance of the half, blazing over the bar from six yards, albeit from a narrow angle.

Leonardo drew another block from Romero before Nikopolidis parried away David Mendes Da Silva's shot.

Lens was enduring a wasteful evening in front of goal and shot wide once more from the edge of the box, but Moussa Dembele was more accurate and drew an unconvincing save from Nikopolidis.

Enzo Maresca's header was gathered by Romero and Dembele saw another effort blocked by Olof Mellberg as the half ended goalless.

AZ were well on top as the second half got under way, with Dembele's effort blocked behind by Michal Zewlakow.

Mendes Da Silva shot wide with an ambitious effort from well over 30 yards, Dembele dragged a left-footed effort across the face of goal and Lens' 20-yard curler also went wide as the Dutch champions struggled to break through.

Brett Holman had another chance from 12 yards but his right-footed effort failed to test Nikopolidis.

The same could not be said of Schaars' 20-yard drive two minutes later though, as the Greek shot-stopper was forced to throw himself to his left to tip the ball around the post.

Lens delivered the corner but Sebastien Pocognoli fouled Zairi, earning the first booking of the match.

AZ boss Koeman introduced Graziano Pelle in place of Dembele as he sought to engineer an opening goal.

But it was Olympiacos who threatened next as keeper Romero, whose place had come under scrutiny in the build-up to the match after a number of recent errors, caused alarm by fumbling Giorgos Galitsios' cross.

Kostas Mitroglou was cautioned for a lunge at Hector Moreno and Raul Bravo followed him into the book for a foul on Pontus Wernbloom.

Leonardo's fiercely struck drive drew a fine save from Romero but Olympiacos could have stolen the points when Dudu fired wide from the edge of the box.

Moreno was booked in stoppage time as AZ's run in the competition spluttered to an end.