In a season of lows this is surely a nadir from which Manchester United now have to recover. To lose away to Olympiakos, the Greek champions of a league some way below the standard of England's top flight, in the easiest of last-16 draws, will cause the most serious postmortem yet.

What is alarming for David Moyes is that United never looked close to scoring. Even towards the end, when Chris Smalling put Robin van Persie in for a clear sight of goal, the usually lethal Dutchman fired over.

Moyes continues to grasp for answers to the big question of why a team that won the title by 11 points last season is so far off the pace this year. While the goals from Alejandro Domínguez and Joel Campbell have not yet knocked United out of the Champions League, whether the manager can get the response of winning by three goals in the second leg at Old Trafford on 19 March has to be in serious doubt.

The players had walked out to the deafening sound of a sold-out Karaiskakis Stadium for an occasion the excited locals were billing as their match of the year. Moyes took a belt-and-braces approach to selection.

With Juan Mata ineligible, he eschewed the more creative talents of Adnan Januzaj, who was not in the match-day squad despite starting in the win at Crystal Palace last weekend, and Shinji Kagawa – named on the bench – for the steadier Antonio Valencia and Ashley Young, either side of Wayne Rooney.

Moyes did retain Rio Ferdinand alongside Nemanja Vidic at centre-back and with Patrice Evra and Smalling also selected, United had the same back four from that visit to Selhurst Park.

As might have been expected, Olympiakos had the early play. Evra was booked for deliberate handball when challenging Campbell, the forward loaned to Olympiakos by Arsenal. While the resulting free-kick amounted to nothing, moments later Vidic's intervention was required to clear lines after successive mistakes from Smalling and Ferdinand.

It was the captain who also made a fine last-ditch tackle on Domínguez after the Argentinian playmaker ran at a visiting defence that parted too easily – an event that was repeated throughout.

All of this indicated how Moyes's team were finding it hard to settle. Indeed, the first half was nearly 20 minutes old before United managed to string a few passes together, though when space was finally fashioned for Valencia the winger's delivery was nowhere near the waiting Rooney.

Most of the play was coming at the other end, with Domínguez finding gaps through which the No10 delighted in slipping through. From one such opening he drove Olympiakos forward and when the ball came to Hernán Pérez he cut inside Smalling and let fly with an effort that missed narrowly. Once more the faultline in United's play was proving to be an inability to control midfield and therefore the contest.

The manner in which Young gave away the ball when a simple pass forward was on midway through the period was illustrative of a problem that has plagued this side all season. It meant Van Persie and Rooney were starved of service, which forced the latter back to pick up play to try to do the job of his midfield.

If the sight of the striker passing straight out of touch was dismal, what happened on 38 minutes was crushing for United. When Giannis Maniatis, the home captain, took aim from 25 yards, it looked speculative. But the dire luck Moyes has attracted all campaign continued as the shot went into a crowd of players in the area and Domínguez fashioned a neat flick to wrong-foot David de Gea and that was 1-0.

The closest United came to an equaliser before the interval derived from a Rooney free-kick. When it was swung in Kostas Manolas's header nearly beat Roberto, the home goalkeeper, but the ball sailed over.

Domínguez's finish meant this was the 16th time in Moyes's inaugural season as manager United had conceded the opening goal. It was also yet another occasion where, at half-time, the Scot had to convince his players they could turn a match their way.

After nine minutes of the second half the task became even harder. Campbell collected the ball about 10 yards outside United's area, evaded Michael Carrick's challenge, then swung a sweet left-foot shot through the ball that beat De Gea to the Spaniard's right.

The roar this brought from the home faithful split the air and added to the shock that swept across the stunned United's players. On the hour Moyes introduced Kagawa for Cleverley and Welbeck for Valencia. But, again, it was Olympiakos who threatened when Olaitan, the lone striker in Míchel's 4-2-3-1, aimed an attempt that came close to beating De Gea and all but consigning United to the most humiliating of exits from the competition.

As it is, Moyes faces questions regarding his selection and how, precisely, he can motivate players who ended this game with belief drained.