I used to be very similar, and still am sometimes with mistakes I think I ought to have caught earlier.

I think it just takes time and constantly reminding yourself that no-one is perfect - we all make mistakes. But that's ok. What's important is how you recover - admit fault, help to fix the problem and try to learn from the experience. It doesn't mean that you won't make other mistakes or even not make the same mistake again but in time you learn other ways of completing the task.

Try not to beat yourself up Mistakes happen and most bosses are very understanding with that. It's not failing.