Home supporters were pouring away from the ground long before the final whistle, their mood more one of resignation than disgust, with West Ham’s Premier League status feeling ever more precarious.

Breathing space from the bottom three has been squeezed to an unnerving three points and, while there is no disgrace in losing to the champions, the manner in which they surrendered was disturbing. Manchester City sauntered to a thrashing and the near silence in the stands was significant.

Considering how many opportunities were created but passed up by Pep Guardiola’s side against the division’s most porous defence, this felt like an escape. City as good as declared in the latter stages, by which time their season’s goal tally was marginally short of a Premier League record having been swollen to 102. Yaya Touré strolled around central midfield for the last 20 minutes while the teenage England youth international Lukas Nmecha led the line on his league debut, and even then the ball rarely left the home side’s half. West Ham, chasing shadows for all but a brief period before the interval, were pummelled into submission.

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David Moyes must somehow raise spirits for Saturday’s trip to Leicester, otherwise this season could have a sting in its tail, not least because Manchester United and the stewardship of Sam Allardyce’s Everton are still to visit. The prospect of their former manager condemning them to the Championship is unthinkable. “I’m not as anxious as when I first came in, because we were in the bottom three then,” said Moyes. “In the main our form here has been pretty good. I’m hoping one of those last two games will turn into points and we also go to Leicester. If we turn one of those into a win, I think we’ll be OK.”

The worries will persist, though, while his team labour like this. It was the kind of masterclass City tend to impose in these parts. Last season they had prospered 4-0 and 5-0 here, playing on West Ham’s insecurities and relishing the wide open spaces on offer. This was merely more of the same, with Raheem Sterling granted the freedom of the right flank by Patrice Evra and Aaron Cresswell while Leroy Sané revelled on the opposite wing. City did not need to innovate or adjust. Other teams may have profited of late from a more aggressive, smothering approach but Moyes had clearly determined his own side lack the dynamism to swarm into such a press and simply sat deeper hoping to survive.

It was never likely to be enough. Only briefly did they flicker into life, Cresswell slamming a free-kick beyond Ederson just before the interval when, in truth, West Ham should have been awarded a penalty after Ilkay Gündoğan’s trip on Edimilson Fernandes. Perhaps if Nicolás Otamendi had been dismissed for a pair of first-half fouls, West Ham might have gained a foothold. Instead they were swept aside, the latest victims of City’s swashbuckling approach.

The most majestic of the visitors’ rewards was their third, scored by Gabriel Jesus early in the second half, the striker initially supplying a wonderfully weighted and incisive pass that sent Sterling scurrying beyond Cresswell and into the penalty area. Just as impressive was the winger’s clarity of thought as he contemplated his centre while West Ham flooded their penalty area. In darted Jesus, unnoticed, to collect with a glorious first touch, disorienting Pablo Zabaleta in the process, and then beat Adrián from close range.

Sterling, whose display warranted a goal, should have earned his side a penalty after Cresswell’s trip but it was his scurry on to Fernandinho’s pass and accurate return for the Brazilian to score that secured the team’s fourth of West Ham’s long afternoon. “Sometimes we judge him on the times he misses but the amount of actions he creates … the assists today, the penalties he wins because he’s so fast and quick,” said Guardiola. “He’s a guy who can go inside, outside, make dribbles. He misses simple balls still and he has to be more aggressive. But he has improved so much.”

West Ham never came close to containing him, for all that there was a sloppiness to City’s first two goals which betrayed the fragility of local confidence. Sané had benefited from Cresswell’s reluctance to engage early on, though the German’s shot required a heavy deflection off Evra to bypass the wrong-footed Adrián. The goalkeeper did better to thwart Sterling before the half-hour, only for City to retrieve the loose ball with Gündoğan supplying Kevin De Bruyne on the overlap. His centre flicked off Adrián’s fingertips and bounced in off Declan Rice and Zabaleta. The Argentinian spent nine years at City, but he took no joy in scoring the hundredth goal of his former club’s campaign.

“They were far better than us, outstandingly good, but we didn’t do well enough in anything we did, really, from the start,” said Moyes. “We didn’t defend as well as we have done against the other big teams this season: filling the box, stopping things. Even if we had put on five subs it may not have made a difference. We couldn’t get close to them.” They will need to be closer to all they confront from now on in.