The Red Devils slid to a woeful 2-0 defeat away in Greece thanks to goals from Alejandro Dominguez and Joel Campbell – on loan at the club from Arsenal.
Having topped their group, many predicted that United’s favourable draw would give them a good chance of reaching the quarter-finals.
However, Olympiakos proved to be tough opposition, despite having sold their star man Kostas Mitroglou to Fulham last month.
After the game, Moyes – who has endured a difficult start to his career at Old Trafford – took the blame for the negative result and the dismal performance from his team:
“It’s the worst we’ve played in Europe, that’s for sure. A really poor performance tonight. We never got going from the start and we didn’t deserve anything because of the way we played tonight,” he is quoted by Sky Sports.
“We just never really got to grips with things. To a man, you could hardly pick anyone out, we just didn’t perform. We came into the game in good form, a good mind set, but we didn’t show that tonight.
“I still didn’t think we were necessarily two goals worse off in the game. We had a shot that gets deflected, but we didn’t offer enough on the night.
“I take responsibility, it’s my team and I’ll always front it up. We didn’t play well tonight and we have to play better. We can do. The one good thing is that there is the second game to go.
“The players are hurting as well. They know how they performed. But there is a team here, that won’t change, and we’ll stick together.
“There is the second game to come and Old Trafford has seen some great nights in the past – I’m looking forward to hopefully seeing another one.”
United were opened up in the first half as Dominguez deflected a fortuitous effort past David de Gea to make it 1-0.
But there was nothing lucky about Olympiakos’ second, which came courtesy of a wonderful long-range effort from Campbell.
Moyes’ men have 90 minutes to turn things around at Old Trafford when the face their Greek foes on 19th March.