If someone doesn’t even know they made a mistake, the desired outcome is for them to realize it, and learn how not to repeat the mistake. Maybe they just needed to be aware that this isn’t what we wanted done. Maybe they need to be more careful during the process. Maybe they need skills training. When you know the outcome and focus on that, you’ll provide what they need so they can get it right from now on.
Just as often, they already know they messed up. Some of the previous paragraph still applies, but we’re going to handle it differently.
First, clarify that you both know what happened. If they say “I messed up” then consider it clarified. Otherwise, if you suspect, but they don’t volunteer, just ask. “Are you aware this isn’t what we wanted here?” Non-confrontational. Just gathering information.
Next, find out if they know where things broke down. Were they careless? Do they need help with mechanics of the task? Was something totally unrelated to the task interfering?
If they’re not sure what happened, or where things broke down, spell it out. Again, since the goal is to help them get it right from now on and not just to make them know how upset you are we do this without rancor. If that means you wait until after you’ve had lunch or taken a short walk, wait. Don’t try to manage their feelings while yours aren’t under control.
If they can tell you what happened and how to fix it, praise their perspicacity, thank them, and move on. If they already know how to get it right from now on, the lesson is already learned. You’re already at the outcome. Any more discussion is like continuing to hammer after the nail is all the way in.
If hammering is your goal, though, take that walk and eat your lunch. Take a breather and come back when you can try for the right outcome.
This all applies when it’s just you, too. Once you know what broke and why, resist the urge to hammer yourself. You’ve learned a valuable lesson. Accept it, appreciate it, and move on. More hammering still doesn’t make any sense.