The Eagles have won six and drawn one of their last eight games – a sequence that has included wins over Chelsea, Arsenal and Liverpool.
Looking ahead to this evening's clash, Allardyce says his charges need to keep pushing in order to mathematically guarantee their Premier League survival.
“The players have done a fantastic job but I just hope they don’t come off the gas and think we've done it,” said the Palace chief, whose side are seven points above the drop zone.
“We took advantage of West Brom on that basis after they had hit 40 points and won that game comfortably 2-0 so I hope the game is big enough (tonight) to ensure that they don’t take their foot off the gas.”
On his side's recent run, the former Sunderland manager added: “We did need that kind of form to get out of trouble and with us still not out of it, even after these results, shows what the players have done to keep fighting.
“(They) have had the desire to get out of the predicament they were in with the guidance of everyone behind the scenes and I must say they have grasped it superbly well.”