Yes most of us expect some form of justice in this life, but we expect it to be fair. For instance a murder and someone that drink drives both did something wrong, but they both get different and appropriate forms of justice. The punishment (as they say) fits the crime. In life there are many things that we can do wrong, but the appropriate form of justice for each thing 'fits the crime'. There's not an answer that covers everything. ie execution for someone that had a parking ticket would be unacceptable, but for someone that committed genocide would be considered acceptable (likewise giving someone a fine for genocide would be equally unacceptable).
Without going in depth if there is a god, then he is all powerful, all loving all just and all judging and the best of judges. Then he will judge best what your accountable for, it's very simple.
so if a god exists, he created all, he tells us via human messengers who and what he is, and that we ought to live our lives to fulfil our purpose for creation. It's like going into exam where the examiner hands you a question paper bit in the other hand also gives you the answer sheet showing you how to pass. Now if your arrogant enough to reject that, then you have no excuse for your failure. Thus if god has provided the test (your life), then given you the intelligence to seek the answers and pass the test, if you do you return to your true home, if not your destined to goto hell, not because god loves for you to be there, but because you were arrogant to reject him and his help. That's justice, ultimate justice, the thing you hold most precious to yourself is a gift from him, if you abuse it then it's your fault, especially if you know where you could end up through such negligence, then that would be tantamount to foolishness. Obviously this is if there is a god.
As for punishments fitting crimes, in this life that's debatable. But the penalty to waste a whole life has a higher stakes.