I don't think it is a matter of attention or discipline exactly. I think kids need responsibilities to become more responsible. They need lots of practice at it, in other words.
I suggest assigning a chore as soon as they are able to do that chore. Starting at three or four, show them something easy like pairing socks and folding washcloths in the clean laundry. You show them how, correct them until they do it just right, then it is their responsibility. Little kids generally love helping! They love to be praised for a job well done. You can make any chore a game or a competition.
What I would never do is put all the responsibility for a living thing on a child. If you have pets, take primary responsibility for them. You can ask a child to feed and water them, every day if necessary, but don't make pet-care a daily unsupervised task like pairing socks. If the child does forget even once the pets will suffer. Always watch to make sure the pet-care is actually getting done. It isn't that you don't trust them! Pets simply are your responsibility, therefore you are obligated to supervise.
As the child gets older, his baby chores can get passed to his younger sibling. My son is an only child, so his chore list just kept growing. A child should be taught to look after himself, part of that means eventually doing all his own chores for himself.
My son has been self- sufficient since he was about ten- picking up after himself. Washing a dish after he uses it. Doing his laundry and keeping his room and bathroom clean. He is very organized and neat in his habits and dress. I think he got that way by doing chores. These skills and attributes will help him manage his time and be more productive in college and in his future job. That is my theory, anyway. So far it seems to be working.