You're probably human if you make mistakes. All humans do. But we don't all deal with them appropriately. If you have done something wrong, here are some suggestions on how to handle the situation:
Accept your own mistakes. You may be frustrated and disappointed with yourself, but there is no point in exacerbating the situation by looking for a scapegoat elsewhere.
Accept that mistakes are part of life. You will always make them. In fact, the busier you are, the more you will make.
Evaluate the situation. Ask yourself specifically:
Does it impact others?
How big is it?
If it's a local mistake that doesn't affect anyone else, and you know how to fix it, do so. No need to tell the whole world.
If the problem impacts others, fix it if you can and tell whoever needs to know, pointing out what you've done to fix it or what you will do. You can also suggest how you will prevent it from happening again.
If you can't fix the problem, find someone who can. Make notes on the solution so that you'll be able to prevent it from happening again or will be able to fix it yourself if it does happen again.
Since the people affected by your mistake may be clients - internal or external - let them know you are sorry. That may take some of the anger out of them.
If you ever make a mistake that will embarrass your boss, make it known to her right away, with an apology and the corrective action. Never let her find out from doing detective work or hearing through the grapevine. She will regard you as untrustworthy and monitor your performance more closely than you will like.
If you make a mistake and can't figure out how to fix it or avoid it the next time, get help. Approach people collaboratively and ask for their ideas. By explaining your problem to someone else, you will often arrive at a solution yourself. If other advice is useful, thank the person who has given it.
Learn from your mistakes, especially the larger ones. Make changes immediately so that the new skills and behaviour become part of your everyday activities.