There is no injustice with God. His justice is never divorced from His righteousness. He never condemns the innocent; He never clears the guilty without repentance; He never punishes with undue severity; He always rewards righteousness. His justice is perfect justice.
He does not require absolutely perfect obedience, or nobody would make it. The blood of Jesus Christ is available to cover us (Revelation 1:5). However, He does not always act with justice because He sometimes acts with mercy. Mercy is not justice, but neither is it injustice, as injustice violates righteousness. Mercy manifests kindness and grace; it does no violence to righteousness.
Those who live by faith must seriously consider God's justice. It constantly reminds us that the wages of sin is death, that sin is disloyalty to God, and that God means what He says. It reminds us of the tremendously precious value of Christ's sacrifice. When we enter into the covenant with God, we are pledging our lives to serve Him in gladness and faithfulness so that He might create us in His image.
God's grace helps to prod us to live continuously by faith. We must know and appreciate His grace without abusing it. His justice is a reality, and so is sin's penalty, but His mercifully given grace overrides both.