The mere existence of something called a "justice system" does not entitle it to respect. It earns respect by satisfying three conditions, corresponding to three points in my discussion in "John Locke: When the Police and Courts Can't or Won't Take Care of Things, People Have the Right to Take the Law Into Their Own Hands": 

1. The judgments rendered by the "justice system" are more more accurate and less biased than judging one's own case would be.  (This is a relatively easy standard to meet, but not one met by all so-called justice systems. See "John Locke: People Must Not Be Judges in Their Own Cases.")
2. The judgments rendered by the "justice system" at least as accurate than that of any available alternative system for judging issues.
3. The "justice system" has the power to deliver justice according to its judgments, or at least has more effective follow-through than any other available source of justice with similar accuracy.

To some extent, imperfection on either condition 2 or 3 can be compensated for by doing well on the other of these two conditions. For example, assuming superiority over having people judge their own cases (not hard), either of

• much better accuracy with almost as good execution of judgments as compared to alternatives, o
• much better execution of judgments with almost as good accuracy as compared to alternatives, 

would entitle a "justice system" to respect as a justice system without shudder quotes.  

Note that sheer power is a big factor in meeting or exceeding condition 3. Thus, as a matter of realpolitik, the nominally designated "justice system" often deserves respect because of its great superiority in execution judgments, as long as its judgments are reasonably good.   

Delivering on judgments has two key components:

• pretrial: hauling malefactors into court as expeditiously as possible
• posttrial: carrying out sentences against malefactors who do not want to be punished 

In the 1st half of section 20 of his 2d Treatise on Government: “On Civil Government”, John Locke emphasizes the pretrial aspect of delivering justice, presumably because of its greater difficulty:  

But when the actual force is over, the state of war ceases between those that are in society, and are equally on both sides subjected to the fair determination of the law; because then there lies open the remedy of appeal for the past injury, and to prevent future harm: but where no such appeal is, as in the state of nature, for want of positive laws, and judges with authority to appeal to, the state of war once begun, continues, with a right to the innocent party to destroy the other whenever he can, until the aggressor offers peace, and desires reconciliation on such terms as may repair any wrongs he has already done, and secure the innocent for the future; 

In the 2d half of section 20, John Locke emphasizes the importance of accuracy and unbiasedness:

nay, where an appeal to the law, and constituted judges, lies open, but the remedy is denied by a manifest perverting of justice, and a bare-faced wresting of the laws to protect or indemnify the violence or injuries of some men, or party of men, there it is hard to imagine any thing but a state of war: for where ever violence is used, and injury done, though by hands appointed to administer justice, it is still violence and injury, however coloured with the name, pretences, or forms of law, the end whereof being to protect and redress the innocent, by an unbiassed application of it, to all who are under it; where ever that is not bona fide done, war is made upon the sufferers, who having no appeal on earth to right them, they are left to the only remedy in such cases, an appeal to heaven.

What is obvious is that accurately delivering justice is a good thing. The nuance here is that, just as a company that does shoddy work not only does a bad thing but also may lose customers, a "justice system" that does shoddy work not only does a bad thing but also may lose respect. A "justice system" that loses people's respect is often spoken of as having lost its "legitimacy." Legitimacy in this sense is the natural law that judges the civil law in action.