I appreciate an employee who comes forward and owns his/her actions. Work together to identify the "solve" and/or actions needed to fix the mistake. Then, learn from it, but then don't dwell. Remember that the first few months of a new job are all about learning, and companies will know that too.
Admit to your mistake professionally and non-emotionally (no need to be crying in the workplace). Explain to your boss why you made the decision/mistake you did. The why is most important.