The 26-year-old made his first Barclays Premier League start of the season at Newcastle on Saturday, but saw chances go begging as the Gunners battled their way to a 1-0 victory over the 10-man Magpies.
Walcott, whose return from a serious knee injury which sidelined him for almost a year has been carefully managed, passed up two glorious first-half opportunities to open the scoring at St James’ Park, including a glaring 32nd-miss with the goal at his mercy.
However, the former Southampton man, who was preferred in attack to Olivier Giroud, is confident the goals will come.
He told Arsenal Player: “I enjoy playing anywhere in the front line and the manager gave me the opportunity today. It’s a shame I couldn’t help him out there by getting those goals, but they’ll come, definitely.
“It was difficult after they went to 10 men, but you need to be able to adapt. But I have been very patient since the knee injury and I just want to play football, that’s all I want to do now, play football for this team because I feel like we can go places this year.
“I had opportunities, but I just didn’t take them. Like I said before, I would on another day. If I came out and got no chances at all, I would be very disappointed, but it’s good that I was in there, and I know I can do better.
“But overall, we got the three points and that’s the most important thing.”
Arsenal had to be patient even after their hosts’ plans were thrown into disarray by the premature departure of striker Aleksandar Mitrovic, who was sent off by referee Andre Marriner after catching midfielder Francis Coquelin late.
Having later viewed television replays of the incident, rival managers Wenger and Steve McClaren differed in their opinions of the challenge, perhaps understandably.
The Frenchman insisted Mitrovic, who has now been booked twice and sent off once in five appearances for the club, had to go even if he had been “maybe a bit unlucky”, but Newcastle head coach McClaren remained puzzled by the decision.
He told nufcTV: “I couldn’t believe the sending off. You can’t win with 10 men. All you can do is show spirit and fight, and they showed that in abundance.
“I couldn’t fault the team, I couldn’t fault what they did, and I didn’t think it was a seven yellow and one red game.
“It’s a football match and you have to compete, and I just feel at times the referee lost a little bit of control.”
Arsenal, who had dominated the early stages, enjoyed the lion’s share of the ball thereafter, although the Magpies’ new-found defensive stubbornness, the excellence of keeper Tim Krul and Walcott’s off-day meant they had to be patient.
They eventually got the breakthrough when the unfortunate Fabricio Coloccini deflected Alex Oxlade-Chamberlain’s 52nd-minute shot past Krul and in off the foot of the far post.
Asked whether his team-mate was claiming the goal, Walcott said with a smile: “We were just actually discussing it and he says he doesn’t think he can. But it’s for him to judge. I would try to get it if I was him, but that’s just me being greedy.”