The fact that Petco offers a replacement in case your bird dies within a month tells you that even they recognize that birds simply get sick sometimes without exhibiting symptoms for a while. I really don't think it's your fault. Who knows what was wrong with your bird initially; things like that happen.
I know you're sad, but I would take advantage of their offer and get another bird.
Things you can watch for with your next one though - if the bird is fluffy every day, inactive, not eating etc. Those are the signs of illness.