The days are long gone when you could offer a penny for someone’s thoughts. In modern football you might need thousands, tens of thousands, millions even, of hard currency. Whatever amount, an insight into Dimitri Payet’s mindset as he learned of West Ham United’s efforts without him would be fascinating. After a half of turgid football that summed up all the difficulties you would imagine a team to have when shorn of a creative leader, a most valuable player, West Ham found enough inspirational verve to leave the pitch with deserved applause ringing in their ears. “It was a great day for us,” enthused Slaven Bilic.

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Never mind the old cliche about changing games, goals can also change moods, and the three that West Ham constructed to swat aside a lacklustre Crystal Palace felt loaded as morale-boosters. Andy Carroll’s acrobatic scissor-kick volley was a spectacle in itself, and, with it, West Ham began to feel very differently about themselves and their predicament.

There is a school of thought that, given the situation, they would do better without their bad egg, in that it would create a new spirit. It is early days to get carried away, but Bilic had abundant reasons to feel his team responded to a hard week superbly. “I can call it one of them that is more than three points. A magnificent result,” he said.

West Ham had been left reeling from the rift with Payet – with the maverick Frenchman excluded since airing his desire to leave the club – and the problem hung heavy in the wintry air. A less than complimentary version of his song did the rounds, suggesting very little sympathy on the part of supporters for his stance, although the general mood inside the stadium revealed more of a weary, resigned disappointment than outright anger. In the match programme, the joint chairman David Sullivan pulled no punches: “We will NOT sell Dimitri in the January transfer market.”

Bilic himself had nothing much to add, saying he would if and when there is a development. He did acknowledge that the situation played a part in “galvanising” the squad. “I told the players we can expect a bit more support and we don’t want to lose it. They wanted to show real commitment and willingness and effort to win the game.”

That took patience. Some nerves for two teams struggling for form played a part in the opening spell. Crystal Palace tested West Ham’s resolve and James Tomkins was aghast to see a stabbed effort from close range squeeze past the post. That was as good as it got for the away side, who crumbled once a tactically adjusted West Ham, shifting to a back four, roused themselves in the second half.

Carroll was in the thick of everything, heading and shooting on sight. The supporting cast more than played their part too, with the enterprise of Sofiane Feghouli, the dash of Manuel Lanzini and the astute passing of Michail Antonio all making a difference. Credit to West Ham for their persistence in continuing to claw at the door until they finally scratched their way through.

When the breakthrough came it triggered a special kind of relief – one born of the adversity that everyone in the ground was well aware of. Deliverance came with a well-worked move, instigated by Mark Noble’s chipped pass into Antonio’s path. He advanced and shifted play across for Feghouli to tap in. The Algerian was elated.

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Carroll then took all that positive emotion and sent it through the roof with a special strike. “He does it in training, although he is normally hitting the post,” Bilic grinned. “I am afraid he will get injured when he does it in training. It was a contender for goal of the season, more than a goal.”

Lanzini added extra sparkle with another sweet strike, latching on to Antonio’s third assist to gently dink the ball over Wayne Hennessey with finesse.

Sam Allardyce looked up at the scoreboard and declared himself “shocked” by what he saw. “I didn’t think it would be one of those where we would collapse, but we did,” he said. “It’s tough for us at the minute. I am still finding out about the players. They are making statements to me by the fact results are not good enough. We haven’t changed that round, which is disappointing for me. The capabilities of not losing are the most important thing to get out of trouble. Once we gifted them the first goal we lost our shape, lost our discipline, started making more mistakes. We have got to be more resilient. They all know they can play better than they do now.” He departed focusing on how he can “coach the ugly side of the game” to give his team a fighting chance.

West Ham have a turning point to build on. Crystal Palace will have to improve to summon up a much-needed one of their own.