The south London club fell behind when Bradley Johnson fired home from 18 yards late in the first half but managed to respond within five minutes when Jason Puncheon scored from the penalty spot after skipper Mile Jedinak was felled by Leroy Fer at a corner.
Palace failed to find a winner in the final eight minutes after Fer was sent off for a second yellow card but Pulis was content with a point in tricky conditions.
"It is in some ways (a good result)," he told Sky Sports.
"The conditions have been very difficult, but we had the better chances and more of the play.
"We could have won the game."
He added: "We mustn't lose games at home, but the conditions played such a big part today. It was as difficult a game that I've seen for a long time.
"It's another point."
The draw leaves Palace sitting 18th on the Premier League table while Norwich dropped to 15th having failed to win in their past five outings.
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