The hosts trailed to Charlie Adam's first-half penalty, but fought back as goals from Theo Walcott, Mesut Ozil and Alex Iwobi secured a 15th consecutive home win against the Potters in all competitions.
"The key was not to let frustration into the game and keep our nerves and our composure," said the Frenchman. "We didn't panic and that's maybe linked with the positive results we've had recently.
"We've given a lot over these days at Basel. We found the resources at Basel to win the game."
Arsenal finished runners-up in the league last season in what many billed as a missed opportunity, with Leicester City claiming a shock title triumph.
Wenger's side have not been crowned champions since 2004, but the 67-year-old hopes they will underline their progress this season.
"We were not too bad last year," he added. "We finished second in the league and we have to show that we've improved in the long term.
"We've created confidence and are ambitious. We need to keep the urgency level high and show that in every single game now.
"We are in there no matter what the results will be. We want to build the momentum and everyone expects you win the game.
"Last season we did very well against the top five and dropped points against the mid-table teams. It's our challenge this year to do well against the mid-table teams."