Pulis took over at Selhurst Park in November with Palace stuck in the bottom three and heading for Premier League relegation.
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A dramatic reversal in form has seen them move clear of safety, though, and a run of four successive wins – against Chelsea, Cardiff City, Aston Villa and Everton – have lifted the club to 11th in the table.
And ahead of Palace's trip to Upton Park to face West Ham on Saturday, Allardyce paid tribute to his opposite number.
"We found that Palace were extremely tough when we played them away [in December]," Allardyce said on Friday.
"We lost the game 1-0 because we couldn't break down a well-drilled defensive outfit.
"They've improved both aspects since then so it will take thought as to how to break them down without leaving the back door open.
"It [Pulis' success] says a lot for the experienced British manager.
"There's enough quality and experience to use in this country and he's proven that quality and experience at Crystal Palace. He's getting the best out of his team."
Despite Pulis' achievements coming in for praise – Allardyce is determined to stop Palace's winning streak.
West Ham are three points below Palace and need a win to keep their realistic hopes of a top-half finish alive.
"What I want to do is make Tony very disappointed on Saturday," Allardyce continued.
"They've overtaken us and we want to get to 40 points on Saturday too."
Allardyce revealed that captain Kevin Nolan will be involved on Saturday after recovering from a hamstring problem.
Defensive pair James Collins (calf) and Joey O'Brien (shoulder) are also set to return to Allardyce's match-day squad.