Bradley Johnson gave the visitors the lead six minutes before the break with a finish from the edge of the area and Palace almost had an even bigger challenge on their hands when Marouane Chamakh narrowly escaped a red card after pushing Wes Hoolahan in the face.
However, soon afterwards, Palace equalised when Jason Puncheon converted a penalty following Leroy Fer's foul on Mile Jedinak.
Palace generally dominated the rest of the match and they had several good opportunities in the second period, but Norwich held on to claim a point - one more than they deserved according to Pulis.
"We should have had the three points," he said. "Overall we had the better chances, the better opportunities and it is the second home game in a row in which we have played in very bad conditions.
"You don't really want that. At home you want to be able to be a little more dominant and I think it was difficult for both teams. The referee also did well, I thought."
Palace were clearly angry late on as referee Mike Dean failed to spot a handball by Johnson just inside the Norwich penalty area, and although Pulis pleaded ignorance regarding the incident, his players were apparently not so neutral.
He added: "The ball sat up, it sat up and caught the wind. That's what happens in these conditions, but they (the players) tell me it was a penalty. I haven't seen it, but they tell me it was a stonewall penalty."
Pulis also discussed the January transfer window, and even though he would not be drawn on whether he is planning to make a permanent move for on-loan Southampton attacker Puncheon, he did admit that the next few weeks hold huge significance for Palace's survival hopes.
"Punch (Puncheon) has done well," he said. "I thought he was one of our better players (against Norwich) and on his day he causes problems for anyone, but the chairman will have to decide that (whether he will be signed permanently).
"Like I have said, the next few weeks are very big for the football club in terms of what we can bring in. They'll be important and we need to get a couple in. If we can then hopefully they'll help us achieve our goals."
