While the Gunners have endured a miserable start to the Premier League season, including an 8-2 defeat at Manchester United, Dortmund's has not been much better and the Bundesliga champions lost 2-1 at home to newly-promoted Hertha Berlin on Saturday.
Dortmund have lost two of their opening five league games and are already five points off the pace of Bayern Munich and Werder Bremen.
And Watzke has demanded a change in attitude against Arsenal.
"We have to go about our business differently," he said in the Bild newspaper.
"We have in the coming days the time and opportunity to bring more sharpness and aggression into our game."