Loft is a far older word than attic. Attics are Attic because they're Greek. In a Greek temple you have lots of big columns. Sometimes you have another smaller set of columns on top. They are characteristic of classical Athenian architecture and Athens was the capital of Attica.
The technical term for a small section at the top of a temple then became a jocular term for the small space above a house. The word was first used in this sense by Daniel Defoe in his Tour of Great Britain, in which he also described Hampstead (which I am leaving) thus:
But it must be confest, 'tis so near heaven, that I dare not say it can be a proper situation, for any but a race of mountaineers...
Attics should be used for storing mad women and cash.
Garrets (which originally meant watchtowers) should be used for storing artists.
The Inky Fool leaving Hampstead