Acknowledgement came out: yours truly wrong? (3,5)
'acknowledgement' is the definition.
(apology or acknowledgement of a wrong)
'came out yours truly wrong?' is the wordplay.
I cannot really see how this works, but
an anagram of 'came' is 'meac' which is present in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for mea culpa that I've seen before include "'I am to blame (3,5)'", "Acknowledgement of one's own fault (Latin)", "Acknowledgment of error or guilt", "An acknowledgement of personal fault or error", "I'm guilty (Latin)".)