The 2-0 loss in the third round at the Emirates means Tim Sherwood's side are now out of both domestic cup competitions, but they still sit fifth in the English top flight.
Spurs will have to wait a week until they can get the game out their system and face the short journey to Selhurst Park as they look to maintain their unbeaten league record under the new first-team coach.
Walker is looking forward rather than dwelling on the defeat and believes there were plenty of positives to take from the London derby loss.
"Losing to the local rivals is always frustrating but we need to pick ourselves up for Palace on Saturday," he told the club's official website.
"We did alright but obviously we didn't come away with the result that we and the fans wanted so it was a disappointment.
"I think we showed a lot of character today, we kept going. The ball just didn't fall for us.
"I thought they (Arsenal) had a few good chances in the first half but we came right back at them in the second."
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