Pulis took over Palace in November 2013 and guided a side that previously appeared relegation certainties to an 11th-place finish in the top flight.
The Welshman left the London club by mutual consent in August last year and has now been tasked with maintaining West Brom's status in the Premier League after assuming the helm from Alan Irvine on New Year's Day.
Former Stoke City boss Pulis takes charge of his first league game as West Brom boss against Hull City on Saturday, and is under no illusions as to the scale of the challenge facing him.
"What we need is to get some results and stay in the Premiership, that's the big aim and the big task," Pulis said.
"It's more difficult [than at Palace] because there's less games. There's less time to put in place what you want to put in place.
"It's different that there might still be complacency because of the name of the football club, it automatically follows that they should be a Premier League club.
"At Palace no one gave us a chance There was more of a siege mentality at Palace.
"Only four wins at home in 2014, it shows that we have to make sure that we do better in our home games. We've got to."
Pulis is keen to add to his squad during the January transfer window, but is eager to ensure that any acquisitions will benefit to a team that sits 17th in the league, just one point above the relegation zone.
"We're looking for some players, the chairman has been very helpful in respect of understanding that we might have to bring some players in," Pulis added.
"It's very easy to go out there and sign players that don't improve the squad, that don't make it better. It's important you get better players in."
