When people make mistakes, the last thing they need is discipline. It's time for encouragement and confidence-building. The job at this point is to restore self-confidence. I think "piling on" when someone is down is one of the worst things any of us can do. It's a standard joke during GE operating reviews that if one of the business CEOs is getting heat and someone in the room jumps on the bandwagon, the staff team will typically pull out the white handkerchief, toss it in the air, and flag the person for piling.
For people (at least those like me, who become embarrassed) the mistake is punishment enough, and people realize that if they continue to make mistakes, something has to happen -- needling people is unnecessary.