Glenn Murray scored twice and Scott Dann found the net - all three goals coming from Jason Puncheon crosses, two of which were corners - making Enner Valencia's late strike nothing more than a consolation.
The hosts could not take advantage of Murray's late dismissal as their winless run was extended to six matches.
"I'm shocked. Our level of performance wasn't where I expected it to be," Allardyce said in quotes reported by the BBC.
"It's disappointing when we've built expectation levels so high at home. It's about the basics, really. If we don't play to our best, we'll struggle.
"We warned the lads about Crystal Palace's set-plays, because 50 per cent of their goals have come from set-plays. And we've conceded from two corners and a free-kick."
Murray was perhaps fortunate not to see red in the first half when, before he scored and having already been booked, he fouled Cheikhou Kouyate.
And Allardyce was not impressed with some of the decisions that went against his side.
He added: "I think Glenn Murray could have been sent off in the first half for the number of fouls he committed.
"He was lucky to stay on for that long. We should have had a penalty for the foul on Diafra Sakho, and it should have been a red card for Mile Jedinak too. That would have made it 3-2, and then you never know."
