Crystal Palace 1-3 West Ham United

West Ham boss Sam Allardyce was asked to provide more entertaining football and his side delivered here

• Palace's struggles continue

• West Ham new boy Mauro Zarate scores on his debut

• Palace lose Joe Ledley to injury in the warm-up

• Hammers boss Sam Allardyce: "We got everything right."

Crystal Palace's turbulent start to the new season continued as they were beaten comfortably by West Ham United at Selhurst Park.

Palace chairman Steve Parish's urgency to appoint a new manager after Tony Pulis left less than 48 hours before the start of the campaign will have increased after a second successive Premier League defeat.

Mauro Zarate scored a spectacular debut goal and Stewart Downing added a second before half-time to put Sam Allardyce's side in control as the Eagles' caretaker manager Keith Millen watched his players struggle desperately.

Marouane Chamakh offered some hope for Palace when he pulled a goal back after the restart but Carlton Cole quickly re-established West Ham's supremacy and they closed out a fully deserved win.

Parish must now turn his attention to ending the turbulence that has overtaken the club since Pulis's departure and the ill-fated move for Malky Mackay.

The move for Mackay was halted after he became embroiled in revelations about texts he shared with Iain Moody while manager at Cardiff City, which subsequently led to Moody's departure as Palace's sporting director.

Tim Sherwood, an early contender to be Eagles' boss, pulled out of the race after Palace moved away from the Mackay appointment and now Parish is left with a major dilemma.

The Eagles chairman must decide whether to hand control to Millen with the transfer window not long off closure or move for an outsider, with former Celtic manager Neil Lennon the latest to be linked with the job after rumours that Pulis might make a dramatic return were dismissed.

The search for a new manager overshadowed Palace's first home game of the season - but even the pre-match warm-up was not without its troubles as Joe Ledley suffered a groin injury and was replaced by Shaun O'Keefe.

The Eagles' passionate support did their best to lift the mood and there were early moments of hope, notably when Chamakh almost got on the end of Martin Kelly's driven cross.

The rot soon set in, however, and West Ham's control led to a splendid opener from Argentine debutant Zarate 11 minutes before the interval, meeting a dropping clearance from a corner with the outside of his right foot to beat Julian Speroni from 20 yards.

Zarate had shown a nasty streak when he left a foot in on the back of O'Keefe's ankle but this was the sort of quality Allardyce - and indeed new attacking coach Teddy Sheringham - would have had in mind from the man who had a loan spell at Birmingham City and arrived from Velez Sarsfield this summer.

West Ham's Stuart Downing capped a fine display with a superb individual goal

Downing matched that three minutes later when he cut in from the right flank before a perfect placement from 20 yards with his left foot beat Speroni low to his right.

James Tomkins headed against the underside of the bar for West Ham in the opening minutes of the second half, and Palace took advantage of the reprieve as Chamakh pulled a goal back with a clinical low finish from the edge of the area.

It was fleeting hope for the hosts though, and West Ham soon restored their two-goal advantage when Cole was given too much time and space in the area and drilled a low effort into the corner.

There was nothing else for West Ham to do other than ensure Palace could not mount any sort of recovery and they did so with ease against a side that looked in desperate need of fresh faces and the sort of inspiration a new manager may be able to provide.

Marouane Chamakh's drilled effort could not prevent consecutive defeats to London opposition for Palace

Crystal Palace caretaker manager Keith Millen: "I won't be watching Match of the Day tonight. I'll recover hopefully and watch it on Sunday.

"It doesn't get any easier. What's gone on this week has been tough for the lads. We never got going at all.

"I'll be speaking to the chairman tomorrow to see what the developments are."

West Ham United manager Sam Allardyce: "We got everything right. We could have scored more than we did.

"We had a plan of attack to break Crystal Palace down with a patient approach.

"We have spent long hours throughout summer trying to acquire the players we have. At the moment they are progressing very well and I hope we can get better."

Mauro Zarate was an unused substitute last week for the Hammers

Palace have conceded two or more goals in their last five Premier League matches

Palace caretaker boss Keith Millen admitted Carlton Cole's goal killed the game

The result will not help caretaker boss Keith Millen's chances of keeping the job

West Ham goalkeeper Adrian was rarely tested

Check out the best photos from today's Premier League games on the BBC Sport Facebook page.