Dear {Recipient},
I'm sorry for {mistake}. I know how {frustrating/upsetting/disappointing/etc.} this is for you and I deeply
apologize for the trouble.
It was an honest mistake, but I take full responsibility for my actions and plan to make amends by {plan}. I
assure you that I've taken the necessary steps to make sure this doesn't happen again. Please let me know if there's anything else I can do to fix my mistake.
Sincerely,
{Your Name}