Tim Sherwood tasted defeat for the first time since he was given the Tottenham job thanks to unanswered goals from Santi Cazorla and Tomas Rosicky.
Apart from an early opportunity for Christian Eriksen, Tottenham created very little going forward and the Gunners never looked like failing to progress to the fourth round of the FA Cup.
Having been on the end of two 5-2 thrashings at the Emirates Stadium, Walker knows the defeat could have been much more painful.
And the Spurs full-back wants the team to bounce back from the defeat by returning to winning ways against Crystal Palace in the Barclays Premier League next week.
"It's disappointing and frustrating to lose to the local rivals," Walker told Spurs TV.
"But we showed a lot of character. We kept going. We have come here previously and (the score) has been higher than 2-0.
"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)."
Tottenham were anything but fantastic on Saturday evening.
Michael Dawson and Vlad Chiriches were easily shown up by the pace of Theo Walcott and the trickery of 18-year-old midfielder Serge Gnabry.
Mousa Dembele and 19-year-old Nabil Bentaleb, who was making his first start, were overran in midfield.
Up front Emmanuel Adebayor, billed as Tottenham's most deadly weapon, rarely featured.
Sherwood was not helped by a lack of options on the bench, though. Tottenham have a crippling injury list and Walker thinks the squad have done a good job over the festive period with limited resources.
"As the gaffer said to us after, we have had limited numbers to play with and credit is due to the lads that have played," said Walker, who scored a stunning north London derby winner at White Hart Lane in October 2011.
"They have picked up results like the win at Manchester United, which was fantastic.
"It is disappointing to lose at Arsenal but we move on and we look forward to Crystal Palace. We need to show the same character that we did at Manchester United to get the three points we need."
Sherwood was without 10 members of his first-team squad on Saturday and his injury problems worsened when Roberto Soldado had to come off in the second half.
Sherwood hopes to have a full-strength squad to choose from by the end of the month.
"Hopefully a lot of them will be back in two or three weeks," the 44-year-old Tottenham manager said.
Having tasted three north London derby defeats as a player, Sherwood knows how difficult it can be to recover from such a loss.
"It's always a massive game for everyone," he said.
"It was just unfortunate for the players and fans that we couldn't get a positive result.
"I thought the performance was okay, but obviously the result is terrible for us."