This seems counter-intuitive, right? Tell your supervisor that you screwed up? Yes, tell everyone that you screwed up. Tell them each time it happens, be honest, and be open about the mistake you made. Don’t try to hide it or blame it on someone else. Attack it head-on and take ownership. Even with bad news, being honest will serve you as a net positive in the long run. For starters, you are working on building trust; this does that. Taking ownership of failures shows management that you understand the mistake. Also, it reinforces that you communicate the good and the bad.
In the end, your mistake would have been found anyhow. Someone would have figured out what went wrong and who was responsible. Heading it off by open communication allows you to navigate the problem from the offensive side. Any other route puts you on the defensive, makes you look like you were covering something up, and breaks down trust.
Openly communicate negative news to build your career.