Dear [Recipient's Name],
I am writing to sincerely apologize for [briefly state the reason for the apology, e.g., the mistake made, the oversight, the delay, etc.]. I fully understand that this has caused you inconvenience and frustration, and I take complete responsibility for my actions.
Upon reflection, I realize that [explain the cause simply, e.g., I failed to double-check the details, I mi*anaged my time, etc.]. This was entirely my fault, and there is no excuse for the error or the negative impact it has had on you.
To address this situation, I have [describe the corrective action taken or proposed, e.g., already corrected the error, re-prioritized the task to complete it immediately, put measures in place to prevent a recurrence]. I will ensure that this does not happen again.
Once again, please accept my deepest apologies for the trouble this has caused. I value our [relationship/partnership/connection] greatly and hope you can forgive this lapse on my part. Please let me know if there is anything further I can do to make things right.
Sincerely,
[Your Name]