A mistake is made unintentionally as in mistaking one person for another or making a mistake in a calculation.
As an excuse for having done something very wrong it seems to me that the work 'mistake' minimises the wrongdoing and lets the speaker off the hook.
If only they would say 'What I did was very wrong and I am very sorry for it and I shall try my best never to do it again because I realise the hurt and injustice that my actions caused'
Instead of which we hear again and again 'I made a mistake'. Or, in other words 'I'm not really responsibe, I did it unintentionally'.
