Microsoft Word is telling me that is isn't.
If it isn't, what is a suitable alternative?
English Language & Usage Stack Exchange is a question and answer site for linguists, etymologists, and serious English language enthusiasts. It only takes a minute to sign up.Sign up to join this community
Carelessly is much more common, and, generally, you should use it, but, yes, uncarefully is a word. Google Books shows it was used by Richard Bulstrode (died 1711) and has been in use ever since.