Goals from Walcott and Olivier Giroud helped the Gunners to a 2-0 win against Stoke City on Saturday, their third victory in five Premier League matches this season.
Wenger's side have been questioned early in the campaign but have conceded just three goals and sit fourth - five points behind leaders Manchester City.
Walcott says that points are all that matter at this stage of the campaign and believes that Arsenal's improving form will be a cause for concern for their fellow title hopefuls.
"When people say we're not playing great - we are starting to get to where we want to be," he told reporters, "and, when we do hit that, people will be more and more worried.
"It's the sign of a good team if you're steady going but still getting the results. It's all about getting three points at this moment in time. No-one is going to remember the start of the season. It's all about how we finish.
"People may not have seen the best of us yet but we are keeping clean sheets and creating a lot of chances. We're especially pleased with the clean sheet. We look very solid and we're not letting many chances against us."
Arsenal visit Dinamo Zagreb in the Champions League on Wednesday before a game against Chelsea on Saturday.