Model on Incompetence

I’m writing this in the heat of the moment, when emotions are raging. I know that EVERY circumstance is considered neutral. But when I encounter circumstances that, after investigation shows that there was obvious negligence or incompetence, how do I dismiss the feelings of anger or disappointment?
C – I assigned a task with very specific details on what needed to be done, but co-worker did not complete. As a result, a package did not go out on time.
T – She wasn’t even remorseful, just dismissed it as, “oh well.” What’s important to me, is not important to others. I now look to be in default, because it was ultimately my responsibility.
F – Angry
A – Hold my tongue, refrain from sending scathing email.
R – I cannot depend on anyone else. Have to do everything myself.
The work environment at my office is already very precarious, and drama abounds. I still need to work amongst this, so I need to correct my emotion around this fast!