Seamus Coleman celebrates scoring the winning goal for Everton against Crystal Palace
The plea came after they dropped into the Premier League danger zone for the first time and surrendered another three points last night.
Facing his second relegation scrap in less than a year after saving Sunderland from a similar calamity last season Allardyce warned that he may not be able to find the reinforcements he needs in this month's transfer window.
He said: "We have to make sure we don't panic and sign players who are not good enough to get us out of trouble.
"If we can find the players we'll sign them, but if we don't, so be it. We all have a desperate need at this end of the table, but there is still a lot more quality to get out of this squad. I just need to get their belief back."
It won't be easy because asif the pressure on Palace wasn't enough beforehand, it was literally piled on them when the result from Anfield filtered through.
Sam Allardyce has urged Crystal Palace to not 'panic' despite their poor form
Swansea's shock win there plonked Palace into the bottom three and effectively made this a must win affair before a ball was kicked.
He couldn't have complained at the way they started. Christian Benteke hit the bar within minutes from a cross that new boy Jeffrey Schlupp laid on for him. Loic Remy looked lively too.
But those defensive frailties were still evident when Everton did break out, and if Wayne Hennessey hadn't been on his toes Ross Barkley could have put the Toffees in front with a shot the keeper did well to tip over.
Barkley had one disallowed for offside after the half hour as well and Hennessey produced another instinctive save to deny Ramiro Funes Mori soon afterwards.
No wonder Allardyce seemed to be chewing his gum more frantically than usual! Or maybe he was just mouthing thanks to Hennessey for three great first half saves that kept Palace in it.
Coleman scoring Everton's winner at Selhurst Park
Close shaves via the efforts of Barkley and Romelu Lukaku didn't calm the Palace nerves after the restart either. And the longer the game went on the more Everton bossed it.
To be honest, Joel Robles didn't have a save to make in the Everton goal until the 79th minute, but he did the business when he had to with a finger tip save from Scott Dan that would have been something of a travesty if the Palace skipper's header had beaten him.
Hennessey heroics continued to keep the impressive visitors at bay until four minutes from time when even he couldn't stop Seamus Coleman giving Everton the match-winner they deserved.
It wasn't without controversy in that Schlupp was crying out for treatment at the the other end. But the ref looked right to carry on playing seeing as how Palace's £12million man was hurt off the field and crawled back on it for attention!
And even those Palace fans who booed the official at the end couldn't deny that Everton deserved the points. They were simply the better side – by a country mile
Crystal Palace: Hennessey; Tomkins, Dann, Delaney; Ward, Cabaye (Ledley 71), McArthur, Puncheon, Schlupp; Benteke, Remy (Lee 61)
Everton: Robles; Holgate, Williams, Mori; Coleman, Davies, Barry (Schneiderlin 59), Baines; Barkley (Jagielka 90), Mirallas (Lookman 71); Lukaku.
Man Of Match: Wayne Hennessey. Produced at least five great saves. If he hadn't Everton would have been out of sight long before they scored.
Referee: A Taylor.