Warning: Broad generalizations ahead. Individual exceptions are likely to exist.
Noxus' social Darwinist "strength above all" mentality has led to a secondary attitude that the weak get what they deserve. In this case, "deserve" isn't meant in a divine or cosmic sense. There's no Spirit of Noxus personally cursing people. (There is Kled, but he doesn't limit himself to the weak and he only has one curse, Being Murdered By Kled.)
Rather, it's believed that certain forms of suffering or inconvenience are a natural consequence of weakness. As a result, no Noxian adhering to this mindset sees themself as weak.
Bad things happening to you, according to this mindset, aren't a consequence of weakness, because you're not weak, right? They're a challenge against which to prove your strength. Failure is just another challenge.
The mindset of constantly striving to prove one's value can lead to great accomplishment, but also puts a lot of pressure on people who make it their way of life, especially if they repeatedly don't "make it."
TL;DR: Noxians probably burn themselves out trying to prove their own value like, a lot.