For Ole Gunnar Solskjær and Manchester United, it was one of those flat and underwhelming performances that highlight how far from the top they have fallen and why the fight to reacquaint themselves with Champions League football this season promises to be so fraught.

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The truth was that West Ham did not have to play too well to bolster their early-season positivity. They were comfortable after Andriy Yarmolenko’s goal just before the interval and the impression was that United could have played all day and failed to score. This was West Ham’s third successive clean sheet in the Premier League and the gloss for them came late on when Aaron Cresswell picked out David de Gea’s top corner with a beautifully executed 25-yard free-kick. At that point, the United inquest could begin.

Solskjær already had injury problems and they would worsen when Marcus Rashford was forced off with a groin complaint just after the hour. But the team he sent out singularly failed to impose themselves. Did they truly believe they would? It did not look that way. They lacked tempo and incision in the final third; it was a performance scarred by sloppiness and errors, and the club’s away-day woes go on. They have lost four and drawn three of their last seven Premier League games away from Old Trafford, their joint-longest run in the competition without a win.

West Ham have not enjoyed a particularly good recent record against the established top six – this was only their fourth victory in 21 fixtures – but the home crowd could bellow out the olés at the end. United’s Ole cringed.

Play Video 0:54 'We hope for better' says Solskjær after Manchester United lose 2-0 to West Ham – video

United suffered here last September in a 3-1 defeat that widened the cracks of the José Mourinho era and this was another ordeal, another embarrassment. Solskjær is determined to give youth its chance, to rebuild and re-energise the squad, and clearly he needs time to realise his vision. The inevitability of the bumps on the way do not lessen the pain.

One of the big questions was always going to be whether Solskjær’s line-up had the creativity to hurt West Ham. Paul Pogba and Anthony Martial were chief among the absentees and from the early stages it was plain that Rashford would have to feed on scraps.

Manuel Pellegrini’s team had a nice balance, with Declan Rice in front of the back four and menace from the flanks in Yarmolenko and Felipe Anderson. They have generally proved a tough nut to crack this season and they took charge upon Yarmolenko’s goal, which was marked by precision and quality. With Andreas Pereira standing off, Mark Noble found Anderson and he was in sync with Yarmolenko. When Anderson flicked the ball on his teammate was already on the move, using his first touch to power away from Harry Maguire and angling a low finish into the far corner.

Facebook Twitter Pinterest Andriy Yarmolenko scores his side’s first goal. Photograph: Rob Newell - CameraSport/CameraSport via Getty Images

United wanted to counterattack but only once in the first half did they threaten to quicken the pulses of their supporters. Daniel James turned sharply to find Rashford and when Issa Diop missed his slide challenge, the United striker had yards to sprint into. Rice, though, had read the danger. He eased back and across to snuff out Rashford, a celebration of understated efficiency.

West Ham sought to keep the back door closed by whatever means necessary, with Angelo Ogbonna taking out Andreas Periera to collect a yellow card as United broke early on and Diop flattening James after misreading a ball. Mark Noble was also high and late on Aaron Wan-Bissaka in the 74th minute and was fortunate to receive only a booking.

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Solskjær sent his players out early for the second half – a telltale sign of managerial dissatisfaction – and things would get worse for him when Rashford pulled up. He had played virtually every minute of United’s season up to that point, including the full game against Astana in the Europa League on Thursday. Had the heavy workload got to him? With Mason Greenwood absent because of tonsillitis, Solskjær sent on Jesse Lingard to lead the line.

West Ham could sit a little deeper after the break and look to counter, an approach that almost bore fruit when Anderson played a give-and-go with Yarmolenko before working De Gea at the near post.

For United, Juan Mata stretched but could not apply a decisive touch to a Pereira cross while Maguire shot low and too close to Lukasz Fabianski on 69 minutes after a corner had been worked to him. It was a bad miss – entirely in keeping with United’s day. Lingard also had a shot blocked by Yarmolenko.

“We deserved the three points,” said Pellegrini, and nobody could argue. “I am happy with everything today. We didn’t allow them to create chances and it’s another clean sheet. We are very consistent.”