A 62nd-minute penalty from Robin van Persie handed David Moyes' men the lead before Wayne Rooney doubled the advantage soon afterwards.
While Pulis had no complaints about the penalty, acknowledging that Marouane Chamakh had fouled Patrice Evra inside the area, he felt that the Premier League champions enjoyed a slice of luck.
"I thought United had a couple of good chances in the first half and on another day they could have scored. They've not had many chances though, the keeper's not made any saves," Pulis said.
"They got a break today - if we'd have got a penalty and gone 1-0 up, it might have been a different game. They got that break and fair play to them.
"Giving them the penalty obviously gave them a lift. I thought it was a penalty - Cham (Chamakh) has come across him.
"He's worked really hard - I don't think he played very well today, but he worked really hard for us and he just made a bad decision, caught Evra and it was a penalty."
Palace, who sit 15th in the Premier League, two points off the relegation zone, are still to welcome Chelsea, Manchester City and Liverpool to Selhurst Park this season.
And Pulis believes his side will need to pick up results against the league's frontrunners if they are to beat the drop.
"We've got a very difficult run of games at home," he continued. "We've got to pick up some points against the top teams."
