The Eagles defeated top-four contenders Everton 3-2 at Goodison Park on Wednesday night to move up to 11th on the table, which has them 10 points clear of the relegation zone.
After the match, Pulis praised his players and the club for the work that had been done since his arrival which is sure to keep the south London club in the top flight for at least another season.
"It's right up there. I am told we had four points (from 12 games) when we went to Hull for the first game I was involved in, and we've got to 40 points with four games to go," told Sky Sports.
"It is really remarkable and a great achievement by the players, who have been absolutely wonderful and have bought into what we've tried to do.
"We've played some very good football tonight and scored some great goals.
"We try and work in a way that we can take the ball off midfield players in positions where the opposition is stretched, and we've got great pace. I thought some of our passing movement was fantastic today."
A proud Pulis added: "I think we are safe, but we have a responsibility to the Premier League to turn up for the next four games.
"I have said to them afterwards that it is a fantastic achievement but we have a responsibility to perform in the next four games."
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