Walcott satisfied with big win
Walcott's contract runs out at the end of the season and he is believed to want a regular starting position before committing his future to the Gunners.
Tottenham took the lead 10 minutes in through Emmanuel Adebayor, but the match turned on its head when the Togolese striker was given his marching orders just seven minutes later for a crude challenge on Santi Cazorla.
From there it was all Arsenal and Walcott caused problems for the Spurs defence throughout the match from the right wing.
He hit a deserved goal in stoppage time after assisting the Gunners' first goal, scored by Per Mertesacker.
"When you've got the big man (Olivier Giroud) up front he's going to cause havoc and when you put Per (Mertesacker) up front, who's just as big, it's going to help my game as well," Walcott told Sky Sports.
"I think last season you could see a lot of glimpses of that, a lot of assists but like I say, I just wanted to play and hopefully I've shown everybody what I can do now."
Walcott believes the Gunners will take great confidence from their win, as they did from a victory by an identical scoreline over Spurs last season
He added: "These games always help us very early in the season and I think if we just showed that kind of ambition and courage in every game, we can climb right up that table now.
"We showed a few people how good we are today and everyone knows we're strong in the dressing room, we showed that today.
"It's going to give us tremendous spirit, we're getting a lot of players back fit now, which will always help, it's nice to see Jack (Wilshere) come on and get a good run out, he's got that different side to his game that we didn't have.
"Everyone's looking bright and looking very confident. Olivier's come in now and people were saying things at the start, but it's always going to take time, but he's shown what a great player he is and I love playing with him at the moment."
Giroud was on target in his first north London derby, and believes he is starting to feel at home at the Emirates, after hitting four goals in his last three games.
"It was an amazing atmosphere this afternoon and I'm very happy to win my first derby," the Frenchman said.
"It was something special for all the fans so I'm proud to have won this derby, it's important for the future to have won this game.
"I feel better and better in this team and we are finding a lot of matches between us which is important for goalscoring and today we showed it's better so we have to keep going and continue to go forward."