Three wins in a row have boosted the Eagles' chances of remaining in the top flight, with the latest victory coming against Watford at Selhurst Park on Saturday.
And Puncheon believes that Allardyce's methods are now bearing fruit, with the Palace midfielder also praising the impact of the club's January additions on the rest of the team.
"The gaffer has always said, and he has been brilliant since he came in, that you always start at 0-0 and if you make sure you don't concede you give yourselves a chance to win the game," he said. "I think the new signings have lifted us and everyone's games as well.
"Mamadou Sakho – he has played at Paris Saint-Germain and for France, and whatever has happened, it is great to have him here."