The local rivals meet at the Emirates Stadium on Sunday in the Premier League.
When asked if Tottenham were now the superior side after spending big this summer, Walcott told the Evening Standard: "Not at all. I feel we're very, very strong.
"Every club are different and they invested their money very well. For us players we just want to do a job on Sunday, we don't care if they have brought in £30m stars.
"They have some very good players and a very good manager but we need to make sure we focus on ourselves. The way we're playing at the moment we believe we can beat anyone."
Arsenal earned a 5-2 win over Spurs when the two teams met at the Emirates Stadium last season.