。
She accused me of being irresponsible.
Literal
She [topic-は] me [object-を] irresponsible [as-だと] accused.
The pattern Xを Yだと + verb-of-judgment ('treat X as Y, accuse X of being Y') is built from を marking the person being judged, the copula だ, and the quotative と marking Y as the content of the judgment. Same frame underlies 彼を天才だと思う ('think of him as a genius') and 彼を犯人だと疑う ('suspect him of being the criminal'). 非難する ('to censure, accuse, condemn') is a fairly formal Sino-Japanese verb — heavier than 責める ('to blame'). 無責任 is a な-adjective built with the negative prefix 無~ on 責任 ('responsibility').