Once upon a time I was working with an SAAS company.  They were  nimble, growing fast, and trying to move to larger enterprise customers.  One of their largest customers experienced some issues…and  panic ensued.  The original issues were resolved quickly but the customer was not happy.  Instead of an organized, well-communicated response to the customer's concerns executives took a shotgun approach,  asking many people in the company for seemingly random bits of information.  Eventually someone included in this widely cast net was able to gather all the threads, point people to already existing information, and create some order out of the chaos.  Unfortunately, by that time the entire organization had been disrupted.

 Panicking is a pretty common reaction and it's hard to predict what will trigger it in any given situation or with any particular person.  Of course, panic rarely results in a useful outcome.

 As project managers, our teams look to us to help figure out how to react.  So…even if you're feeling panicky, you'll need to take a deep breath and do the duck thing (calm on top, paddle like heck underneath).

Here's what you can do to avoid or avert panic:

1. First, DON'T PANIC yourself (or at least get control of it fast).  Take a deep breath and proceed.
2. Call a halt to whatever panic reactions are already in process.  Everyone wants to try to fix things and it will be hard to trace root cause or determine additional causes if everyone is doing this in a vacuum.  It helps to remember that it's not your responsibility to solve the problem - it's your responsibility to lead a team of experts to a solution.
3. Get all the involved together (a strike team).  Don't invite anyone not directly involved in either the problem or the solution - that will only slow you down.  The key to limiting the attendance without issues is to communicate what's happening to a wide audience and keep that audience posted. 
4. Lead the strike team to a plan. (The first plan might just be data gathering).  Set a time to get back together to review.
5. Send the strike team off to do their thing.
6. Publicize the plan so no one else starts to try to solve the problem on their own.  Let people know when the next update will be coming.  Don't wait too long between updates; even if no progress has been made everyone wants to know the problem is still being worked.
7. Repeat steps 4-6 until you reach a resolution
8. Hold a post-mortem for both the problem and the response to the problem

If you gain control of the situation early you can avoid a cascading organizational panic attack, benefit from having the right people with the right knowledge addressing the situation, and come to a successful resolution.  One of the best things about this method is that it works for pretty much any situation.  Of course, if you have a family emergency you'll be a bit more informal about things, but the step still work - don't panic, get everyone together (virtually is fine), let everyone know what's happening.

 But the first step is always DON'T PANIC.