Errors WILL happen on client accounts. Here are next steps.
1.) Listen to them vent.
2.) Apologize and admit responsibility.
3.) Solve the problem.
Once the problem is solved, then work on "don't let this happen again" resolutions. The anger from the client is distracting enough. Don't compound the "problem solving" activities and panic employees with YOUR anger.
More times than not, this will work.