Toffees midfielder Ross Barkley struck the crossbar prior to James McCarthy being sent off for fouls on Yohan Cabaye and Yannick Bolasie, while Palace’s best chance fell to Jason Puncheon, who was denied by Everton goalkeeper Joel Robles.
A draw built on Saturday’s victory over struggling Norwich, while Palace are a solitary win away from smashing through the 40-point barrier, with five league matches of the season remaining.
“That point is crucial, as I don’t think those bottom three can catch us now,” said Pardew. “I would have taken four points from these last two games but, wow, we should have won.
“Although I’m frustrated, I’m pleased with another good performance. I want my offensive players to be a bit hotter, but I’m pleased with two clean sheets.”
Everton are now winless in five league matches and, after a difficult campaign which has seen manager Roberto Martinez criticised from a section of the club’s fanbase, sit 12th, two points ahead of Palace.