A well-worked goal from Wilfried Bony gave the hosts a deserved lead after quarter of an hour, before Palace skipper Mile Jedinak was on hand to smash home from the penalty spot 10 minutes later.
Palace secured a hard-earned Premier League point with a spirited second-half display, but Warnock was left to lament their bad start.
"The first 20 minutes was as bad as I've seen since I've been at the club. We just couldn't put two passes together and it was really poor," he said.
"It's a hard place here. I saw them batter Arsenal a couple of weeks ago so I knew how difficult it was going to be but I thought the lads responded.
"I thought we had a great chance at 1-1 to score, and then at the end I tried to be a little bit positive by bringing Wilfried [Zaha] on because I thought we could pinch it.
"You have to give us credit really because after the first 20 minutes a lot of other teams could have laid down but I thought we played some control football in the second half and we looked a threat on the break.
"A little more quality in certain areas and we might have pinched it."
Swansea boss Garry Monk said he was unsure about Martin Atkinson's decision to award Palace a penalty after Jonjo Shelvey had brought down Marouane Chamakh.
However, his views were not shared by Warnock.
The former QPR manager added: "I think it was a penalty. Obviously there might be other people that will say it’s not but I just thought he did enough to stop him from turning into the ball and even Shelvey didn't complain."