There had been few chances for either side until Robin van Persie opened the scoring from the penalty spot in the 62nd minute following a foul by Marouane Chamakh on Patrice Evra.
Evra then crossed for Rooney to score United's second with an excellent strike six minutes later, leaving Pulis to bemoan just a couple of lapses.
He agreed with referee Michael Oliver's penalty decision and lamented the fact his six-goal striker Chamakh had had a rare off-night when the Londoners were looking to extend their unbeaten home record.
Newcastle had been the last team to take all three points from Selhurst Park when winning 3-0 on December 21.
"I thought it was a penalty," Pulis said. "Cham's come across and he's made a bad decision and caught Evra and it's a penalty.
"He's worked really hard but the disappointing thing with Marouane at times, and I think he'd be the first to admit it, is that he gave the ball away a lot today.
"He's not normally that kind of player. He's a very good footballer."
Pulis added: "We knew the longer the game went on, with it being 0-0, the more opportunities we'd get because United would press on to us.
"But then they got a couple of goals and the second one, we could have done better with that as well."
It was only Palace's second home defeat since Pulis replaced Ian Holloway at Selhurst Park in November but the Welshman still acknowledges his side are in the fight for a survival.
"Every game whether it's home or away matters," he said.
"We have to start collecting the points. We're in it with 12 other teams. It will go right to the end. Whether it's against the top four or five, there's always three points. We have to scrap and fight for everything against every team.
"Today was disappointing. That [the penalty] gave United the leg up they were looking for."