Not everyone has the same idea regarding the concept on Justice...as an ideal, I think it would be safe to say we might espouse the same frame of mind w/regard to justice but you raise an interesting question- what does one do when the law cannot/does not mete out justice, as we see it?
Perception being what it is, what one man sees as injustice could very well be attributed to any number of things, apathy on the part of the parties involved, misrepresentation of facts, you name it, it has happened at some point in the past. Justice should be blind, but humans are not. This is why court proceedings are a lot like daytime tv- loaded w/drama, the principles are usually turned out in their Sunday best with strategies focused on obfuscating the other side, we've all seen it. You have to ask yourself, how on earth can Justice be done when there's so much that gets in the way of it?
I doubt there could ever be a perfect justice system, and not just because humans are rendering the judgments- but that there are way too many loopholes, fallacies that allow the discerning mind to make use of; especially when someone can successfully sue a corporation because they burned themselves on a cup of coffee they purchased from a franchisee...that one burns me in particular, no pun intended.
I think that as far as getting a fair shake goes, you're much better off in an American courtroom than in any other...Canada being the possible exception.
Of course...if they allowed certain litigated disputes to be resolved by personal combat, I'd bet we'd see those drop to near-nothing...no one wants to actually get harmed in the process of hoodwinking the justice system, right?