As soon as you find out you made a mistake, tell your boss. Don't try to hide your mistake.
Come up with a plan to fix your mistake and present it to your boss. Be very clear about what you think you should do.
There will be some people who argue that it's not their fault. However, It won't help you to point fingers at others, even if they do share responsibility for the mistake.
Apologize for the mistake but don't continue to berate yourself. If you keep calling attention to your mistake, that is what people will remember. You want everyone to focus on your actions AFTER the mistake.
Try to fix the mistake on your own time but do not work overtime unless you receive permission from your boss to do so.