Dear [Name],
I want to start by apologizing for my inadequate management of [situation]. As your manager, I understand that I was responsible for ensuring that [situation] was handled in a timely and efficient manner. Unfortunately, I failed to do so, and for that, I am truly sorry.
My lack of attention to this situation has caused [consequences], and I understand that this has caused you and other members of the team to feel frustrated and disappointed. I take full responsibility for my actions and accept that I should have done more to ensure that this situation was managed properly.
I have since taken the necessary steps to ensure that this situation is handled in the most efficient way possible. I have also taken the time to review my management style and have identified areas that need improvement. I am now taking the necessary steps to ensure that I am better equipped to handle situations like this in the future.
Once again, I apologize for my inadequate management of [situation]. I understand that my actions have caused frustration and disappointment, and I want to assure you that I am doing my best to ensure that such a situation does not occur again.
Sincerely,
[Your Name]