Exculpation, n.
Etymology: [Cf. LL. exculpatio.]
The act of exculpating from alleged fault or crime; that which exculpates; excuse. These robbers, however, were men who might have made out a strong case in exculpation of themselves. Southey.
Shades of meaning
Fernald has no entry of its own for exculpation; he lists it under apology.
Where he writes about it:
Defense, exculpation, justification, and vindication are more properly antonyms than synonyms of apology in its modern sense, and should be so given, but for their connection with its historic usage. — from apology