IPA: /ˌʌnɪkˈsɛpʃənəbli/
KK: /ʌnɪkˈsɛpʃənəbli/
In a way that is completely acceptable or without any faults.
The project was completed unexceptionably, meeting all the requirements.
Unexceptionably → It is formed from "un-" (meaning not), "exception" (from Latin "excipere", meaning to take out or exclude), and "-ably" (meaning in a manner). The word means in a manner that is not subject to exception or criticism.
Think of 'not' ('un-') allowing anything to be 'excluded' ('exception') — that's why unexceptionably means something is done in a way that cannot be criticized.