Palace were given no chance of survival by most three months ago but only Liverpool and Arsenal have collected more points at home since the New Year.
That sequence has seen Palace move three points and two places above the relegation zone but Pulis knows they will face another stern test against Southampton on Saturday.
With Chelsea, Manchester City and Liverpool still to visit Selhurst Park this season the pressure is on, but Pulis remains in confident mood.
"We know how tough this run is for us," he said.
"We have got it as tough as anybody in the bottom 10 but we will get our heads down and work as hard as we can.
"There are 10 or 11 teams still fighting for their lives and we are ahead of the game in a lot of respects because we are still in with a chance and nobody gave us that chance a short time ago.
"It is very difficult to stop the players looking at things. You can get so confused and uptight and lose a lot of energy worrying about things you can't affect."
Meanwhile, Pulis believes Southampton deserve credit for the number of players that have come through their academy - Calum Chambers, James Ward-Prowse, Adam Lallana, Sam Gallagher and England's latest cap Luke Shaw among them.
"They have done it consistently for a long time," he said.
"They haven't just stumbled over it. They have the jigsaw sorted out and all the pieces are in the right place, we don't do that a lot in this country.
"I know a little about the club and there are people who have been there for years and years. They have a good scouting set-up and the people who work there, even before you become a professional, are very good lads.
"They don't worry about just the technical side of it, they look at attitude, commitment and responsibility. Most of the lads who have come out of that club are not only good players, they are good lads."