Walcott was given the chance to play up front by manager Arsene Wenger and repaid his manager's faith by slotting in the fifth goal, following Lukas Podolski's strike and a Santi Cazorla hat-trick.
When asked about recent criticism following last week's exit from the Capital One Cup, Walcott said: "We showed people the true Arsenal.
"We don't take notice of the outside. We're a big family and we know our quality and that we're good enough.
"I enjoyed playing up front and the boss gave me that opportunity.
"I thought I did very well and the players around me always make my job easier."
Adam Le Fondre and Jimmy Kebe denied Arsenal a clean sheet but Gunners midfielder Jack Wilshere was quick to echo his team-mate's sentiments.
He said: "I think we saw the old Arsenal in patches here.
"We need to tighten up defensively as we gave two sloppy goals away."
Referring to the Bradford game, he added: "We're disappointed, naturally. It's a natural feeling of disappointment when you lose to a lower-league team."
Of last night's opposition, Wilshere said: "They're fighting relegation so we knew they would be up for it.
"Theo and Santi were different class and the boys around them helped as well."
Walcott is in talks over a contract extension at Arsenal.