Santi Cazorla opened the scoring from the penalty spot despite Danny Welbeck appearing to be fouled outside the box by Pape Souare, before Olivier Giroud doubled the lead prior to the break amid suspicions of offside.
While Glenn Murray pulled one back late on before hitting the post deep into stoppage time, Palace suffered a third defeat of Pardew's tenure.
However, the former Newcastle United boss felt their showing was actually the best since he arrived in January.
"We took a tactical decision to take the game to Arsenal today," Pardew explained. "The first goal is a mistake by Pape, he should do better, and yet the call is tough on us because it looks like the incident happened outside the box.
"We find ourselves 1-0 down but we continued with the gameplan and I was pleased with the reaction. It's probably the best we've played since I've been manager.
"The second goal is offside and that should be made that call.
"I had more of a problem with the second goal than the first - it's a minute before half-time and you've got to get that call right.
"The one that hits the post and goes into the keeper's hands just summed our day up really, it wasn't to be."
