The England international was in sparkling form as the Gunners demolished north London rivals Spurs on Saturday, while Olivier Giroud insists he is feeling better at the club
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.
The England international caused havoc for the Spurs defence throughout the match from the right wing and hit a deserved goal in stoppage time after assisting the Gunners' first goal, scored by Per Mertesacker.
He told Sky Sports: "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.
"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."
Emmanuel Adebayor was sent off for Tottenham, after netting the game's opening goal, but the Arsenal attacker believes the Gunners would have put in a good performance, whether the Togo international had been dismissed or not.
"I didn't really see it," Walcott said. "But I think he did go in quite two-footed but the referee's made the decision and you'd have to ask him what he felt.
"I think even if they did have 11 men I think we showed great pace and we never gave up."
Olivier 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 added.
"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."