The England international broke the deadlock at the Emirates Stadium just after the half hour mark after latching on to a sublime pass from Mesut Ozil to shrug off the challenge from Potters defender Marc Muniesa before slotting the ball past Jack Butland and into the back of the net.
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However, the 26-year-old missed a host of chances throughout his time on the pitch and was guilty of missing two sitters in the first-half and he acknowledges he must improve in order to keep his place in the starting XI.
“I was pleased with that goal,” he told reporters after the game.
“Luckily I managed to grab one out of my many chances. I was disappointed because I should have got many, many more, but I’m getting the chances so I’m happy with that.”
“When you get given the opportunity you have to try to grab the goals when you can. We create chances so we just have to put them away. We’re starting to get back to the old Arsenal,” Walcott added.
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Walcott is likely to rotate the centre-forward role with Olivier Giroud, who also netted against City, in the near future as another option to lead the line in Danny Welbeck was ruled out for at least three months after undergoing knee surgery at the start of September.