If you moved out without providing at least 30 days notice, you owed them another month's rent--the issue isn't whether you lived there any longer, since people can and do rent space they are not currently occupying. Rather, the issue is whether you provided sufficient notice or not. If you failed to provide sufficient notice to properly terminate your tenancy--at least 30 days (unless you lease was coindentally expiring when you moved out), though often more than that is required--they would be entitled to at least one more month's rent.