Pulis had taken the Eagles out of the bottom three after taking over at Selhurst Park in November but a home point against fellow strugglers Norwich was not enough to stop them sliding back in to the drop zone.
Bradley Johnson had opened the scoring with a well-taken long-range effort in poor conditions in south London before Jason Puncheon equalised with a penalty late in the first half.
Leroy Fer, who was booked for conceding the spot-kick, was sent off late on for picking up a second caution but Palace could not find a way though.
With Fulham beating West Ham at Craven Cottage the point saw Palace fall below Rene Meulensteen's side but Pulis is not about to hit the panic button.
"The end of the season is when it counts," he said.
"It is not at Christmas or new year. The most important thing if you focus on that. The window opens so it gives you an opportunity to wheel and deal; move a few out and a few in, which hopefully will help us."
After an even first half ended all square, Palace were the more dangerous side after the break and Pulis felt the hosts were deserving of a win as the rain continued to lash Selhurst Park.
"Overall I think we should have three points," he said.
"That is the second game running we've played games in very poor conditions, which made it a lottery.
"You don't want that at home; you want the advantage of being at home. I thought the referee did well under the conditions."