The Eagles' secured survival on Wednesday night with a win at Champions League-chasing Everton, with the former Manchester United boss one of just two who backed the role
The 56-year-old has inspired a stunning turnaround in fortunes at Selhurst Park, with the club now guaranteed Premier League survival after reaching 40 points with a 3-2 triumph at Everton.
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"Did I have doubts about taking it? It was difficult. I met [Palace chairman] Steve Parish and spoke to Steve about four or five times and I didn't feel it was right," he told reporters.
"I looked at it and everyone I spoke to said it was a difficult one. Alex Ferguson and Peter Coates, my old chairman at Stoke, they were the only two who said to take it. They were two very good judges!
"I hadn't seen Palace play, but I enjoy a challenge. It's in my nature to stand up and try to march people forward and we've done that.
"The players have been wonderful and you can't do it without them. They have responded to us and given us everything."
Pulis, who transformed Stoke from a mid-table Championship side into an established top-flight outfit under Coates, believes wingers Jason Puncheon and Yannick Bolasie have been key to Palace's resurgence.
"Bolasie and Puncheon have been brilliant for us," he added. "They've been the catalyst to everything we've done really. They are a non-stop threat.
"The two of them have been journeymen in some respects but they've found their home with us."