'anime-inspired' originates from English as a compound of the elements 'anime' and 'inspired'. 'anime' itself was borrowed from Japanese 'anime' (a shortening of English 'animation'), where 'anime' meant 'animation'; 'inspired' originates from Latin 'inspirare', where the prefix 'in-' meant 'into' and 'spirare' meant 'to breathe'.

'anime' entered English via Japanese in the 20th century as a borrowing of the shortened form of 'animation'; 'inspired' entered English earlier via Old French 'inspirer' from Latin 'inspirare'. The modern compound 'anime-inspired' developed by combining the borrowed noun 'anime' with the English past-participial adjective 'inspired' to mean 'influenced by anime'.

Originally 'anime' denoted 'animation' (Japanese usage) and 'inspired' originally carried the sense 'breathed into' (Latin). Over time 'inspired' shifted to 'motivated' or 'influenced', and the compound came to mean 'influenced by the style or elements of anime'.