'non-specifically' is formed from the negative prefix 'non-' (from Latin 'non', meaning 'not') combined with 'specific' (from Late Latin 'specificus').

'specific' came into English via Late Latin 'specificus' and Medieval/Modern French 'spécifique'; the adverb 'specifically' was formed by adding the adverbial suffix '-ally'/'-ly', and 'non-' was later prefixed to create 'non-specific' and then 'non-specifically'.

Originally 'specific' related to 'a species' or 'kind' (from Latin 'species'); over time it came to mean 'clearly defined' or 'particular', so 'non-specifically' developed to mean 'not in a clearly defined or particular way.'