How can Miller explain the justice in the play?
I think the point that Miller is trying to make is the fact that justice is lost in this play during that era. Since the United States has had a Constitution, the ideas of the separation between church and state and the accused being innocent until proven guilty have reigned in our courtrooms and these circumstances don't happen. I think Miller used this tale in a cautionary fashion to remind us that we must be careful in our own accusations of other people. We must consider if we just believe something to be true or if it really is true. Then, we must act accordingly.
The only sense of justice I see in this play is for John Proctor. He had a sincere conviction between right and wrong and did not want to do wrong but as most humans, he did have moments of error. Elizabeth's strong last words about John prove that John came full circle as a character. John did not want to lie to the magistrates in the end just so that John could live. He had already committed enough sin in his life that made him feel terrible. He wanted to give the truth and tell the magistrates for sure that he did not have any sort of compact with the Devil. He did this knowing that the price for the truth was his life. Was this just? No. But as Elizabeth said, "He have his goodness now." She means at least he died with a free conscience and in living righteously in death he may be free in the afterlife.