'anti-excitatory' is formed from the prefix 'anti-' (from Greek 'anti' meaning 'against') combined with 'excitatory', which derives from Latin 'excitare' meaning 'to rouse', plus the adjectival suffix '-ory'.

'excitatory' developed from Latin 'excitare' → Late Latin/Medieval Latin forms → Old/Middle English 'excite' and later English 'excitatory'; the modern compound 'anti-excitatory' was created by combining 'anti-' with 'excitatory' to denote opposition to excitation.

Originally the roots signified 'against' + 'to rouse'; in modern usage the compound specifically denotes an action or property that opposes or reduces excitation (especially neural excitation).