IPA: /ɪnˈɛk.sjʊ.zə.bli/
KK: /ɪnˈɛkʃəsəbli/
In a way that cannot be justified or excused; without any valid reason.
He acted inexcusably by ignoring the rules.
Inexcusably → It is formed from "in-" (meaning not), "excusare" (from Latin, meaning to excuse), and "-ably" (meaning in a manner). The word "inexcusably" means in a manner that cannot be excused or justified.
Think of 'not' ('in-') being able to 'excuse' ('excusare') something — that's why inexcusably means something that cannot be justified.