Fernando Torres opened the scoring for the Blues in the 16th minute at Stamford Bridge, before Marouane Chamakh levelled with a neat volley just before the half-hour mark.
Ramires quickly put Jose Mourinho's side back in front with a sensational strike but the result remained in doubt until the final whistle as Palace produced a battling performance.
While Pulis was happy to acknowledge Chelsea's quality after the final whistle, he could also take some positives from the way Palace played.
He was happy to have put such a strong team under pressure and only disappointed that they could not take any of the chances they made.
"We gave Chelsea a run for their money today," Pulis told Sky Sports.
"In the last minute we were still pushing forward trying to get that goal that would have got us something out of the game.
"Chelsea are a top, top side. They played some smashing stuff today and they move the ball very quickly.
"I thought we stood off them a little bit first half. But second half we pushed up and on to them, and we took the game to them at times and created good opportunities ourselves.
"We just needed a bit of luck. We got it at one end with Chelsea missing some chances but we needed it at the other."
Pulis also paid tribute to Chamakh, adding: "He has bought into what we want to do and the way we want to do it, and his effort and commitment have been fantastic.
"You add the little bit of quality that he has got, and he has been a good player for us."