It is not only completely legal, but encouraged that you drink in public in New Orleans. So you committed no crime even if you felt naughty doing that.
My first time to New Orleans, we were walking down Bourbon Street and they were literally shoving cups of beer into our hands. Of course, we did walk nearly the entire street, turned around and skeedaddled back when we hit the darkened section with all the rainbow flags < shudder > and headed back to the freebie spots and frequented them.