When a company is working at 100% capacity (sometimes with no clear processes), breakdowns are bound to occur. This is not your fault. You are allowed to make mistakes at work. A well managed company works steadily at 80% capacity (and has clear processes); that way, staff can make mistakes, handle unplanned work (emergencies), and sustain operations.
Coming soon: a blog post about how to maintain your own 80% when the rest of the company appears to be working at 100%.