Goals in each half from Alejandro Dominguez and Joel Campbell sealed victory for the Greek champions, leaving United with a difficult task of progressing to the Champions League quarter-finals.
Moyes’ men registered just one shot on target on Tuesday evening and the Scot admits his players deserved to lose the fixture.
"It was a really poor performance,” the Scot said. "I didn't see that performance coming. The one good thing is there's still a second game.
"Old Trafford's seen some great nights in the past and we'll hopefully see another one.
"I take responsibility, it's my team and we have to play better.
"That's the worst we've played in Europe, we didn't deserve to get anything.
"We just never really got to grips with things and to a man you could hardly pick any body out. We just didn't perform tonight.
"We came into the game on good form, with a good mindset, but it didn't show.
"I still didn't think we were necessarily two goals worse off in the game but we didn't offer enough on the night to create a goal."The Champions League represents Moyes' last realistic chance of winning a major trophy in his first season at Old Trafford, with the Red Devils out of both domestic cup competitons and trailing Premier League leaders Chelsea by 15 points.