Sam Allardyce's return to West Ham, though not, of course, to the Upton Park he left behind 20 months ago, ended in defeat and left him without a victory in five games as manager of Crystal Palace, who sit outside the relegation places on goal difference alone.

They had looked the more likely side in a dull first half but were overwhelmed afterwards as Andy Carroll, a striker always admired by Allardyce when fit, became the dominant figure. His spectacular scissors kick may well have been the goal of the day anywhere and helped push his side to a more comfortable mid-table position.

Mikhail Antonio made all three goals and little Manuel Lanzini suggested there could be life after Dimitri Payet if need be. Statistically West Ham win twice as many games with Payet in the side as without him but this performance belied the figures and expectations.

There was no sign of the French playmaker, who has been taking advantage of the transfer window to announce his intention of returning to his homeland regardless of the five-year contract signed only last January before his starring role at Euro 2016.

Andy Carroll takes a shot on goal (Getty)

West Ham now face the classic dilemma of a key player who wants to better himself elsewhere: stand firm until the end of the window and hope to get the best out of him for the rest of the season – possibly by promising a move in the summer – or cash in now, taking a sufficiently large fee for all-round improvement to the squad.

Home supporters showed where their loyalties lie on the issue, chanting support from the start for Bilic in his hard-line stance. “I heard that support from the crowd but it is not personally for me it is for the decision we made,” he said. “There is nothing more to say about it.”

It was repeated in the 27th minute, marking Payet's squad number. At that moment they might have been celebrating a goal, for Carroll had just volleyed their only chance of the first half over the bar from Mark Noble's cross.

Yohan Cabaye tussles to take the ball off Pedro Obiang (Getty)

Allardyce meanwhile had kept his distance - and what a distance it is from the dugouts to the touchline. Once he had made the long march to the touchline to have a word, Palace began to make the better chances. Yohan Cabaye's smart shot from 20 yards required Darren Randolph – back in the side after Adrian conceded five against Manchester City – to make the game's first save; Noble's foul brought a free-kick by Andros Townsend that was jabbed wide across goal by James Tomkins; and from another Townsend cross, Jason Puncheon at the far post could not quite turn the ball in.

From the start of the second half, however, when Antonio was pushed further forward as second striker in a change of formation, there was a welcome flurry of goal-mouth incident as Carroll began to harass the visiting defence more menacingly. He hit three decent shots in the first quarter of an hour as well as almost beating former team-mate Tomkins to Feghouli's cross.

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He then won a free-kick in a perfect position for Payet; Lanzini clipped it over the bar, but the pressure was building and in the 67th minute the home side scored. Noble sent Antonio through in his new position in the inside-left channel to veer wide of goalkeeper Wayne Hennessey and lay a pass square for Feghouli to tap in his first league goal.

Palace sent on Chelsea loanee Loic Remy, Lee Chung-Yong and new signing Jeffrey Schlupp from Leicester City but Carroll left his old manager looking rueful by meeting Antonio's centre sideways on with a classic left-footed scissors which he called his best-ever goal.

James Collins complains to referee Neil Swarbrick (Getty)

“It's a contender for goal of the season,” Bilic said. “He does it in training and I'm not happy because I'm afraid he's going to get injured.”

Four minutes from the end Antonio completed a hat-trick of assists by sending through Lanzini, who always scores against Palace, to do so again.

Allardyce must now try for that first win against another of his old clubs, Bolton wanderers, in Tuesday's FA Cup replay at Selhurst Park.

“For 70 minutes we didn't look in any trouble,” he said. “Once we gifted them the first goal we lost our shape and discipline.”

West Ham (4-2-3-1): Randolph; Collins, Reid, Ogbonna (Byram, 46), Cresswell; Noble, Obiang; Antonio, Feghouli, Lanzini (Fernandes, 87); Carroll.

Crystal Palace (4-2-3-1): Hennessey; Tomkins, Dann, Delaney, Ward; McArthur (Lee,69), Ledley (Schlupp, 80); Townsend (Remy,69), Cabaye, Puncheon; Benteke.