I am writing to apologize for missing the deadline for the [project/task]. I understand that this is unacceptable and I take full responsibility for my mistake.
I understand that this project was important and that missing the deadline has caused you considerable inconvenience and distress. I can only imagine how frustrated and disappointed you must feel and I want to express my deepest apologies.
I had planned to complete the task on time and had worked hard to do so. Unfortunately, I encountered some unexpected difficulties which I was unable to overcome. I should have communicated with you earlier to let you know that I was having difficulties and that I might not be able to meet the deadline.
I understand that this is not an excuse and that I should have done more to ensure that the task was completed on time. I am truly sorry for my mistake and I want to assure you that I will do everything I can to make sure that this does not happen again in the future.
I am willing to do whatever is necessary to make up for my mistake. I am available to work extra hours to ensure that the project is completed as soon as possible. I am also willing to take on additional tasks to help make up for the delay.
Once again, I apologize for missing the deadline and I want to assure you that I will do everything I can to make sure that this does not happen again.