What I am learning to do is to not take it personally. I guess it's stating the obvious to say that the universe is not out to get me (or any particular person), but there you are.
The thing is that you're right, it is senseless and random, but it's not that some are "made to suffer more than others" -- as far as the universe goes, there's no intention behind who suffers more than others -- it's just that in the world we live in, the system is so complex and therefore chaotic that we can't predict who gets hurt in that tsunami and who escapes unscathed.
The way I understand the Way is to accept the reality of the situation: it is what it is; and then be as nimble as possible in living within that reality.
It's only "senseless" if we impart no sense to it. That is, the universe doesn't seem to concern itself with human sensibilities -- we provide the meaning, meaning on a human scale. The universe itself is empty of human meaning -- and some of us perhaps overdo it when giving it human meaning (something to be wary of) -- but we can quite mindfully do our best to give the world we live in meaning that is consistent with what we see around us. For me it's this: yes, horrible things happen -- sometimes as random chance physical phenomenon, but even more often through human ignorance and blindness -- what part of that can I do anything about? Not the tsunamis (though early warning systems could help if that was my field) but human ignorance and blindness to the way things work, that I can have some small effect on, starting with working on my own.