Dear [Recipient],
I am writing to apologize for my failure to complete the task that you had assigned to me. I understand that my inability to finish the task has caused you inconvenience and I deeply regret it.
I take full responsibility for my mistake and I understand that it is unacceptable for me to have not completed the task. I had taken on the task with the intention of completing it on time, but due to a series of unfortunate events, I was unable to do so.
I understand that I have let you down and I want to assure you that this will not happen again. I have taken steps to ensure that I am better prepared for future tasks and that I will be able to complete them on time. I am also willing to take on additional tasks to make up for my mistake.
I understand that words are not enough to make up for my mistake and I am willing to take whatever steps necessary to make sure that this does not happen again. I am truly sorry for my mistake and I hope that you can forgive me.
Sincerely,
[Your Name]