No, Arsenal need to comprehensively beat a direct rival away from home, to have confidence.
In case it's what you're insinuating; the 10 men you had doesn't take anything away from the victory, it adds to it in fact. You went down to 10 men because of Arsenal's superiority and the deficiencies in your team. If it was an incorrect or fluke sending off, then it would be right to say Arsenal's victory wasn't
that impressive, but it wasn't.
Anyway, on a lighter note, some Stoke City fans today: