I feel tragedies very deeply, and think a lot about how the people involved must be feeling. However, I don't cry, or wail, or go on FB, as I think this is wasted emotion and effort. What I do instead is make a (usually small, unfortunately) donation to a relevant charity, as I figure that sitting hundreds or thousands of miles away emoting isn't going to help anyone, but a pound or two WILL.
Dunno if this is middle class European "throw money at a problem so I don't have to feel guilty at winning in the lottery of life" behaviour, but it's money - it does things, it buys practical help. Doesn't stop me thinking and feeling for the people, but it means I know someone somewhere has a blanket, or some soup, or a vaccination.
Some friends of mine are prone to emoting online, and I ask them to focus not so much on how they feel, but what they can do. Sign a petition, write to an MP, donate some old clothes, a quid...50p....