Palace host second-placed Tottenham on Wednesday, having won six and drawn one of their last eight games -- a run only bettered by Tottenham, who have won seven in a row.
What is more, Palace have beaten Chelsea and Liverpool away during that period as well as Arsenal at home.
They are still below the notional safety target of 40 points though and Allardyce, who began the season as England manager but was sacked after a newspaper caught him on camera offering advice on how get round FA rules on transfers, remains wary.
"Some of the best results I've had in my long career as a Premier League manager, Chelsea and Liverpool away, Arsenal at home," he told a news conference on Tuesday.
"We can't take our foot off the gas and think we've done it. That's how we beat West Brom -- they hit 40 points and relaxed.
"It's probably the best spell I've had as a manager, in terms of an eight-game period, given who we've beaten and how we've done it."
Palace will be without defender James Tomkins who was injured in Sunday's 2-1 victory at Liverpool.
(Reporting by Martyn Herman; Editing by Hugh Lawson)
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