The Gunners looked unstoppable as they cruised into the last eight, despite missing key players including influential skipper Cesc Fabregas.
Walcott said: "Five-nil will have an effect on other clubs - hopefully they will be wary of us.
"Arsenal is a big club - every club that plays us fears us.
"We've got great people going forward, great defenders. You look at the way we played, we took all our chances and defended very well. Thomas [Vermaelen] was throwing his body in places where you wouldn't want to see. It was teamwork and it went fantastically well."