What happened in Nepal is terrible. The Tsunami was terrible. Natural disasters show us how powerless we are, and how much destruction can be made, without any human involvment (other than the philosophical and hypothetical in terms of "what could we have done to predict this, and what steps could we have taken to minimize impact")
I think it can be justified to to turn off the tv and avert your gaze a little, it is just too frightening. We cant do anything, unless we are trained especially to help in such cases. Throwing money at the problem is all we realistically can do. So lets make sure we give if we can, if our situation allows it. And if we cant afford to donate, then that is fine too.
Where I dont think we can turn a blind eye, is when disasters are man -made, then we need to really look closely, feel, empathize, and see it as our role to see what we can do in our lives that can prevent such bad things. What our role as parents are, how we instruct our young. How we act to one another to avoid causing each other distress. Bullying, ignorance, racism, lack of understanding of each-others faith, sexual orientation. We can be the best we can be, and teach our children to act with kindness and without prejudice. That is what we can do.
So OP, you can turn off the TV to avoid watching footage from Nepal, but look at what is happening in Baltimore, look at what is happening in Syria, IS gaining a stronghold in Africa. These are examples of events that we as humans need to read about and watch, and where we cannot turn a blind eye. Even if we dont act, we need to open our hears and our mind to events that shape our world.