Yes, it is natural to seek vengeance.
I mean, if were a father of one of the kids gunned down by Mr. Breivik on July 22, 2011 - well, the first thing I would do on the day he is released from prison (those super-"humane" Scandinavian laws...) is to sink as many rounds into his chest as I could, before cops bring me down.
This is not how you build or sustain civilization. This is how you destroy it.
Do I know what "justice" is? How? Oh, sure, it says so-and-so in a sacred book - the Torah, if I am lucky; the Complete Works of Parteigenosse Lenin/Hitler/Mao - if I was born on the wrong side of the fence....
Screw that. I do not know what's "justice". Have I ever been to another person's brain? Felt what he or she feels? Knew what she or he knows? Suffered from exactly the same kind of madness?
Justice is impossible. Period. Unless you are the all-knowing God. Are you?