"In fact, we have a very clear policy on mistakes - when you make one, be honest about it up front. You won't get disciplined bot you'll clean up your mess. I'll help you if you need it but you're doing the donkey work. Just don't make the same mistake twice."
Yep, mistakes happen, learn from them, find what can be done to prevent them and move on.
The only unforgivable sin (or at least sin you'll get major shit for) is trying to cover up your mistake rather than admit it, especially if it results in your boss being caught out unaware of the issue. Never seen a colleague fired for making a mistake, but have seen someone fired for lying about it.