Goals from Andros Townsend, Yohan Cabaye and Luka Milivojevic inflicted a fourth successive away defeat in the Premier League on the Gunners, and in truth their winning margin could have been more.
At the other end, Wayne Hennessey had one of his easier nights in the Palace goal as Arsenal failed to muster a single shot on target in the second half.
The full-time whistle brought more angry reactions from Arsenal's travelling support and Walcott acknowledged the players had been well off the pace.
"The biggest thing would be letting the fans down," the Gunners skipper for the night told Sky Sports.
"That's not Arsenal at all. Tonight wasn't us. We're very disappointed and have let the fans down. We have to respond.
"We thought we had bounced back from that bad patch with the draw against Manchester City and win against West Ham. It doesn't look like it after this.
"We don't go out there to lose games, we work the best we can. Tonight it didn't happen. We can only apologise."
While that may have placated some Arsenal fans, Walcott's admission that Palace had wanted victory more will not have gone down well.
He added: "You could tell they wanted it more. You could sense that from the kick-off. It was an uphill battle."
The defeat leaves Arsenal seven points adrift of fourth-placed Manchester City, putting their hopes of Champions League qualification in serious jeopardy.