As boss, your job is to cushion the blow that comes to your team from outside it (no matter how richly that blow is deserved). This means standing up for people who've done dumb things, and taking responsibility for the dumb things that were done. As the Manager, the team is your responsibility, and anything stupid any particular member does is also your responsibility.
Your team should feel that you will watch out for them, and give them room to make mistakes. This is also the same charitable spirit that will make you fly like an eagle when they have successes. The flip side is that when they screw up, you feel that screw up rather intimately, too.
You can talk to those people, but I recommend not coming to them right after you've been berated with their issues (I have a whole blog post on not talking to people when you're cranky).
Instead, I recommend the following:
1) Get all the facts. The person coming down on you like a ton of bricks who would prefer to come down on your employee like a ton of bricks may not be at his or her most rational. Get the details and then tell them that you'll handle it and get back to them, and send them away from your team. Next, investigate. Before going directly to the person or persons involved, talk to people tertiary to the event and try to get an impersonal view of what happened. This may mean interviewing people, it may mean reading log files, whatever, do it.
2) Send an email to the appropriate folks after the first step in your investigation. Your boss, the person or persons who are upset and their bosses, as needed. Let them know you are investigating and what progress you've made so far, and that you will be following up by interviewing those involved. Be polite, be professional, and admit nothing about the allegations other than your true concern to alleviate the distress of the parties involved. If this springs up several more emails, this really only makes the distressed party look bad, and, to a certain degree, takes some heat off of whatever the stupid thing was. It may also reveal additional details for your investigation...people tell their bosses things that they don't tell other people and you might find additional witnesses or locations for facts, or even facts themselves in the subsequent email thread.
3) Track down any additional resources garnered and collect the data.
4) For issues that involve more than one person, interview each of them individually.
5) Ask the person to describe what they thought happened and what they were thinking when it happened. Get details from them about additional witnesses and information, and check their stories against the data you've already got; I don't mean "but X said the exact opposite, what do you say now?" prisoner-of-war interrogation, I mean, "X remembers it this way, any idea why?" You are that person's manager and you are, therefore, on their side. They should know that. They should also know that whatever hell they've rained down will also be raining on you, so you need the facts.
6) Once you've got the facts from your interview, collect more data from the clues you received from directly speaking with these folks.
7) Set up a meeting with the person or persons in questions who did the stupid thing and go over what you've found out with them. Explain why the choices might not have been the best, and ask how they could make better choices next time. Ask them for any additional input on the process before you turn over your results to the parties in question. Ask them if they can think of any relief that might please the parties who were aggravated and write their suggestions down.
8) Follow up with your boss, the person(s) affected, and their bosses. Give the details of your investigation as devoid of emotion as possible. Explain the learnings from the issue and the steps being taken to allay the issues resulting. Be clear that you are handling any additional recrimination/punishment for your team yourself, and thank them all for their patience. I recommend concluding via email; if you get additional emails, just keep politely explaining it's been dealt with and thank them for their involvement and honesty.
9) Talk to the members of your team who have screwed up and put in place a plan to avoid the same kind of screw up in the future. If they feel they deserve it, give them a duty that no one really likes to make up for it, and then, END THE DISCUSSION. The incident never needs to be spoken of again. They're adults. You are an adult. They've learned what they can. Let everyone move on.
A brief aside here--this doesn't mean you don't go over with that person that this was bad and you didn't enjoy getting in trouble for their mess. But it does mean that this is not the central theme on which you're working. You are a part of a team, this is the part you accepted when you accepted being their manager, and the results you want are the situation resolved, never to come up again, not to vent your anger (as fun as that sometimes sounds when you're in the middle of something like this).
It's your job as a manager to help people recover from and learn from their mistakes, not to make them afraid to try new things for fear of making mistakes. Its also your job to protect them from people who are emotionally charged on the issue--even, and especially, if your team is responsible for the issue, those people go to you, not your team. Its your job to shelter them from the rain and to lift them up into the sunshine, and to help them know the difference so they can improve themselves, the team, and the overall project.
If, for some reason, you, yourself are agitated by this whole business, you are welcome to communicate that before the close of things, but it is not ever to be the central theme. Finding and fixing the problem, and then making sure it never happens again are the take-aways. Not venting your frustration. Your team needs to trust you, and the quickest way to erode that trust is to let emotions get in the way of productive work.
Your team will learn and they will respect you for protecting them from the fall out. They only want to be treated fairly and they will do good work. There are always the occasional bad apples, and, of course, you'll have to deal with them over time. But when you look at your team you need to know that they are going to screw up, but, they are a team of people that you are happy to support in their screw ups because they will learn from it and get better as a team because of it.