"It will be far from easy," warned the Scot before kick-off. But in the end, for Olympiacos, it was.
The Champions League round of last 16 had progressed much as expected, with Borussia Dortmund continuing the trend that saw the winners of the group stages - and those playing away from home first - build comfortable leads to take back with them. United proved themselves the predictable exception, with another hapless display of defending from a unit that looks consistently bewildered when opposition attackers drive towards goal.
The tie is far from over, of course, and it would be churlish to write off Manchester United at Old Trafford, but for Moyes' side to progress they would almost certainly have to keep a clean sheet, something that currently looks far beyond them at that level. A goal for the visitors in three weeks time would leave United needing four.
"We've lost a game," said Michael Carrick, the United midfielder. "We came here hoping to win but we are not out of the tie. It's not ideal.
"We had good possession in the first half without penetrating through their lines but at the same time they didn't cause us any problems. We didn't start the second half well and that put us on the back foot. We are not getting results and as players we have to take that on the chin.
"You're looking for me to blame someone but everyone at the club is judged by results."
Alejandro Dominguez's clever backheel had put the Greeks ahead in the first half and from then on in Moyes' side rarely looked like being able to get back into the match.
And this Greek tragedy had a particular bitter twist, from a passingly familiar foe. It was an Arsenal player who stuck in the last knife, early in the second half. Joel Campbell, who is on loan from Arsene Wenger's side, scored a wonderful, curling strike to leave United on the brink of European humiliation.
The winger has not kicked a ball for Arsenal since he signed in 2011, but he just about kept his balance after nutmegging Carrick before curling a stunning shot around Rio Ferdinand and the sprawling David De Gea from 20 yards.
The man on the loud hailer behind the home goal bellowed and the fans demanded their team go in for the kill. Michael Olaitan nearly obliged, firing a 20-yard shot just wide of a flat-footed De Gea. Campbell received a standing ovation when he came off moments later as Moyes brought on Shinji Kagawa and Danny Welbeck, but they could not make the difference.
For United, Wayne Rooney worked tirelessly, as is his wont, and Nemanja Vidic put in a solid performance at the back. But the midfield, as it has done for much of this season, looked awfully pedestrian amid a boomingly intimidating atmosphere inside the Karaiskakis Stadium.
Olympiacos, who are bidding to make the last eight for only the second time, made a mockery of the away side's billing as favourites. And without Juan Mata - cup-tied - and Adnan Januzaj, who was bizarrely overlooked, United looked toothless in attack.
''That's the worst we've played in Europe, we didn't deserve to get anything," said an understandably disappointed Moyes. "I didn't see that level of performance coming. I take responsibility, we have to play better. The players are hurting."