In my experience, life is easier when you admit your mistakes without business speak, and just take the blame (for example: "I" instead of "We"). I've written a lot of mea culpas for mistakes which impacted customers, and the more direct and transparent I was, the better responses I always got.

You made a mistake, you know you made a mistake. Admit it, apologize, and move on. Your excuses or context probably aren't going to help your cause.