When Pulis succeeded Ian Holloway at Selhurst Park in November, the Eagles had secured only four points and already seemed destined for relegation.
Instead, Saturday's 2-2 draw with Fulham completed an 11th-place finish with 45 points that Pulis - now a candidate for manager of the year - believes the club had no right to expect.
"If you'd said to me when I came in that the game against Fulham would decide whether we stay up, I would have taken it," he said.
"Actually, I'd have chopped your hands off
What we've done and what we've achieved has been absolutely remarkable
The supporters and players have been wonderful.
"If you look at the stats from when I came in it shows what a great achievement this season has been.
"But one stat not to forget is that we managed to finish 11th with the smallest budget in this league.
"This football club has massively overachieved and everyone should take great credit, it has been a great ride."
Pulis has been linked with Newcastle amid reports he will replace Alan Pardew, but his immediate concern is discussing with chairman Steve Parrish how to take Palace forward.
"I'm not in a position of power, I'm not after power, but there are certain things that must go on to make a club successful," he said.
"I had a good chat with Steve last Thursday and we'll meet again this week and go through things.
"That's the way to do it and fingers crossed, hopefully we'll both get to where we want to be."
Fulham's relegation from the Premier League had already been confirmed by their 4-1 defeat at Stoke eight days earlier.
They at least depart for the Sky Bet Championship with Chris David's stunning stoppage-time equaliser the last meaningful act of their 13 years in the top flight.
Felix Magath fielded a young team against Palace and the Whites boss declared the club would rely heavily on its academy in the Championship.
"We know we have a lot to do and we'll do it
We have to discuss and analyse the situation and team," he said.
"The team I selected against Crystal Palace is a sign that we'll change something in the future.
"I will take care of our youth players because we have a good youth academy, but in the last few years they haven't played much for the senior team
We'll bring the academy players into the Fulham team.
"We have to look at the money because we are not able to pay players big wages
We are looking for young players now."
Source : PA
Source: PA