'antidotally' originates from English by formation from the adjective 'antidotal' + the adverbial suffix '-ly', ultimately tracing back to Latin 'antidotum' and Greek 'ἀντίδοτον' (antídoton), from 'ἀντί' (anti-) meaning 'against' and 'δίδωμι' (didōmi) / the root 'dō-' meaning 'to give'.

'antidotum' (Latin) comes from Greek 'ἀντίδοτον' (antídoton, 'that which is given against'); the English noun 'antidote' entered via Old French/Middle English, the adjective 'antidotal' developed by adding '-al', and the adverb 'antidotally' formed later by adding '-ly' to the adjective.

Initially it referred specifically to something 'given against' a poison; over time it broadened to mean any counteractive remedy or, figuratively, anything that neutralizes or offsets an undesirable effect. 'Antidotally' now describes the manner of acting as such a countermeasure.