It depends on your definition of "Justice"
Hypothetical scenario: if I knock out your tooth, and you — in response — knock out one of mine mine, has justice been achieved?
In the stone age, the answer would have been "Yes", because of the stone age definition of justice: if you harm someone, you will be made to suffer the same harm, summarized as "an eye for an eye".
This is known as Mirror Punishment and is a form of Retributive Justice, i.e. if you do something wrong, there will be retribution. Note that this is also a form of Proportional Justice.
In modern times, however, the answer is not as clear cut, because these days justice is much less about retribution — though in the eye of the public, retribution is often desired — and more focused on Reconciliation, Reparation, Rehabilitation, and also Prevention and Protection Of The Innocent.
Also note that modern justice is also still very concerned with proportionality.
So, if we look at the goals, and measure...
- Were the innocent protected?
- Was crime prevented?
- Was reconciliation achieved?
- Was the victim repaired/compensated for their damages?
- Was the perpetrator successfully rehabilitated and reintroduced into society?
- Were the consequences proportional to the offense committed?
...and, to a lesser degree...
- Was there satisfactory retribution?
...and find that one or more of the points above were not achieved, then we have a failure of justice, i.e. an injustice .
Which then brings us to the question: when is there a legal reason for such a failure?
Here we risk failing the "book test", which means that if the answer can fill a whole book, it is too long for Stack Exchange. And since we can — with the sub-questions enumerated above — cover all of modern jurisprudence (the theory of justice) — which is not just a book but a whole university education in and of itself — I will have to do a shortcut by genericising a bit, which is as follows:
Whenever law, law-making, and/or the enforcement of law, is the reason for a failure of any of the above, then that is a legal failing that has led to an injustice.
This then begs the question: is there anything that is not a "legal failing" when justice is not achieved? This I have no answer to, one could argue both yes, and no, depending on how far you are willing to give the legal system power to act on you.
We could — for instance — institute a benign Big Brother society, by simply abolishing a few rights, such as freedom of movement, the right to privacy, and the right to free expression and/or the right to free thought. With these things out of the way, we could achieve many more of the points enumerated above. But I do believe many think that this is not a cost we are willing to pay. Instead, we are more willing to let the legal system partially fail, rather than give up these rights.
With this in mind, we end up with the odd concept of "acceptable failures", i.e. we have to let the justice system fail to — for instance — prosecute, judge and sentence a perpetrator, if we cannot — with high enough certainty — establish their guilt.
