I should have known that if the question came from the Gita, the answer would probably be there, too. (I think I said before that I’m impatient, and this is pretty typical for me.)
I read a little from it every evening before I go to sleep. After Krishna tells Arjuna about selfless action, he proceeds to talk about meditation. And he says something that answers the questions I had about how to feel in bad situations:
When a person responds to the joys and sorrows of others as if they were his own, he has attained the highest state of spiritual union.
So feeling deeply sad for people affected by disasters, whether natural and massive or man-made and personal is all part of realizing that you are connected to each and every one of those people.
I don’t think I’ve ever heard it put in such a clear, understandable way before. Next time, I’m going to keep reading before I worry.