Pulis has overseen an impressive turnaround in fortunes since arriving at Selhurst Park in November.
Palace were among the favourites for relegation when the Welshman took the reins, but now sit two points outside the bottom three in 16th place.
However, Pulis is aware there is still plenty of work ahead if the club are to avoid an immediate return to the Championship.
"We've had such a great run that people forget this is the Premier League and this is going to be really tough," he said on Friday.
"We've 10 games to go and we're playing teams who have been in it, seen it and done it before.
"I made one reference after the Southampton game - they brought on a midfield player (Victor Wanyama) who they spent £12 million on.
"That's what we're competing against every week and you have to keep your feet on the ground."
Palace face a key game on Saturday as they travel to Sunderland, one of the sides in the relegation zone.
Pulis is not taking the challenge lightly even though Sunderland have lost four of their last five matches in all competitions.
"The hard work and the effort that the lads have put in has been fantastic - the next two months they have to do the same and, if anything, raise it a little bit more," he added.
"People look at Sunderland's position and say it's a six-pointer but every game is an important game for this football club."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.