Oh it totally drops away! It's not a permanent record type thing at all. It's something CEOs and ADs are very nervous of because of financial or reputational repercussions but it's not the end of the world. Sometimes it's not even the fault of the person involved, it's a training issue.
I've been involved in 3 in 10 years, where either my training of someone wasn't up to scratch, or I wasn't closely enough checking what new staff were doing.
What does your line manager say? We're they supposed to check your output?
My honest advice would be to be completely transparent, say you realise what happened was a problem, and lay out what you will now put in place to ensure it doesn't happen again - sanity checks/a checking system/a process improvement with an additional step to avoid it reoccurring.
Also offer to send an email to any involved parties explaining that a clerical error has occurred, no detrimental impact has happened, and processes have been put in place to avoid in future, and explain what the steps are.
In my workplace we'd then absolutely move on. Shit happens, you're human, we've probably all been involved in a fuck up! I certainly have.