Spurs lost 2-0 to their local rivals told with goals in each half from Santi Cazorla and Tomas Rosicky at the Emirates Stadium.
Apart from an early opportunity for Christian Eriksen, Tottenham created very little going forward and the home side never looked like failing to progress to the fourth round.
Having been on the end of two 5-2 thrashings on the same ground, Walker knows the defeat could have been much more painful.
"It's disappointing and frustrating to lose to the local rivals," Walker said.
"But we showed a lot of character. We kept going. We have come here previously and it has been higher than 2-0."
Walker is looking to return to winning ways next weekend when Tottenham return to Premier League action against Crystal Palace at White Hart Lane.
"We have got to pick ourselves up. We have a big game on Saturday, a London derby and we need to get the three points because we have been fantastic (in the league)," he added.