The Welshman was appointed boss after Ian Holloway left Selhurst Park and is preparing Palace for Tuesday's match with Hull after guiding the Eagles out of the relegation zone.
When asked about the speculation over his position, Pulis, who has never been relegated in his management career, said: "I'm not one of those people. I spent 10 years at Stoke.
"I'll say this now, the supporters have been absolutely wonderful, absolutely fantastic.
"There would have to be a massive reason to leave and let them down. I'd find that very difficult to do."
Pulis was appointed on the day Palace beat Hull at the KC Stadium in November, with the team under the caretaker control of Keith Millen.
In his 12 games in all competitions since, Pulis has overseen five wins and a draw; four of the victories have come in the Premier League to take Palace two points clear of the drop zone entering the Hull contest.
The Eagles boss has often spoken of the need to recruit and denied further speculation linking him with moves for FC Twente's Danish defender Andreas Bjelland and Brondby striker Simon Makienok.
"I don't even know them," Pulis said. "If you said there's £1million if you knew what position they played in, I wouldn't have a clue."
Pulis is actively seeking reinforcements, though.
He added: "We're trying to get players in and make the squad stronger for the last 16 games of the season.
"We've been working very, very hard to identify to bring players in and I'm sure it will be busy come the end of the week.
"I think we need to bring in four or five players and I'm not talking about spending money on one of them that is extortionate, I'm talking about trying to bring players in who have a little bit of experience in the Premier League but also have something to prove.
"We're just hoping that one or two things will drop for us. The important thing is that everybody understands and recognises the task ahead.
"It's a smashing group of players here, they've worked their socks off for one another.
"We don't want to bring in people here who are going to stroll around. We want people coming in here who will roll their sleeves up.
"I've come to the football club and I like to pick my own players. If I have to pick players on a certain budget, I will do so.
"We have done fantastically well over the last few months, but that's just the start of it. We know our level and what we can and what we can't do.
"Hopefully by the end of the week we'll bring some players in."
A return for Manchester United winger Wilfred Zaha, who appears likely to sign for Cardiff on loan, was not possible as Palace already have two players on loan in Jason Puncheon and Cameron Jerome.
Pulis also confirmed Palace have enquired after Wigan's Ivan Ramis, but that Cardiff may beat the Eagles to the defender.
"We were interested in the lad but Cardiff made him a better offer so he went down to them," Pulis said.
Pulis is likely to have to shuffle his defence against Hull as Jonny Parr is expected be out with the concussion he sustained in the FA Cup loss at Wigan.