Lucas Paqueta's volley gave them hope of a late comeback, but an equaliser did not come as West Ham's 17-match unbeaten run in Europe cam to an end.
Here's how David Moyes's side rated in Greece...
Drafted in with Lukasz Fabianski ill. No chance for either goal.
Nervy start as West Ham struggled to settle in raucous atmosphere.
Ought to have been more at home than any of his team-mates, returning to the city of his birth, but frustrating lack of composure in possession.
Angelo Ogbonna 3
Dreadful attempt at clearance that didn't need to be made ended in own-goal and crucial Olympiacos cushion before half-time. Booked and maybe a touch fortunate not to receive a second yellow soon after.
Made a decent chance for Ings after the break and did drive the Hammers forward on occasion.
Tomas Soucek 5
Had started well in breaking up the midfield play but too passive as Fortounis waltzed through midfield to score opener. Nuisance presence up top late on.
James Ward-Prowse 5
Like Soucek, guilty of standing off for the home side's opening goal.
West Ham's likeliest outlet on the counter-attack but faded. Deserves a chance in a full-strength side.
Ineffective on the left flank, down which Olympiacos had plenty of joy. Failed to get tight enough to Rodinei for cross which led to second goal.
Said Benrahma 5
Surprisingly deployed in the No10 role but experiment didn't really work.
Danny Ings 4
Fed off scraps, though did have a decent chance deep into first-half stoppage time. Spooned over from Emerson's cross after the break.
Lucas Paqueta (Fornals 57') 7
Absolutely walloped home on the volley. Terrific hit.
Jarrod Bowen (Benrahma 58') 6
Unable to continue his terrific run of goals on the road.
Michail Antonio (Ings 58') 6
Made his presence felt with barge on Porozo, which earned booking. Cross created indecision for Paqueta goal.
Maxwel Cornet (Kudus 72') 5
Couldn't really get into the game down the left.
Edson Alvarez (Ward-Prowse 72') 6
Twisted inside out by Alexandropoulos but did just enough to put midfielder off a third.