First, you need to own your mistake. Don’t get defensive or try to play the blame game. Acknowledge that something is wrong and show that you’re going to put your energy toward fixing the problem. Then, when the dust has settled, go back to your boss and apologize, explaining that everything is okay now, but that you recognize your mistake and won’t let it happen again.
Sometimes you will notice a mistake before your boss has. If you can fix it before he ever finds out about it, great, no harm done. But if it’s something that’s going to affect him, alert him to the problem yourself and have a solution ready to go. This will show that you’re being proactive and will help minimize anger.
The solution-oriented approach is always the best way to handle mistakes. This tactic also works when the mistake is not your fault. If you can come up with solutions to someone else’s mistake instead of blaming him and letting him deal with it, you’ll help that person save face, something he will remember and appreciate for a long time.
Always be the problem-solver in a bad situation. Don’t freak out, place blame, or give up and do nothing. By remaining calm and poised yet determined to fix a mistake, you’ll impress your colleagues and establish yourself as a reliable, trustworthy person.