It's undeniable that we are all sinners and as long as we sin, there will be no peace in our hearts (and in the world). Without God, sinners try to ignore and forget their sins. They seek escape in worldly pleasures or consolation from others, but the stains on their souls remain. God is the only one who can take away sins ~ there are just no other means!
In Matthew 16, Jesus said to Peter, "I will give you the keys to the kingdom of heaven. Whatever you bind on earth shall be bound in heaven; and whatever you loose on earth shall be be loosed in heaven." For us Catholics, we just take advantage of the Sacrament of Reconciliation instituted by the Lord to get ourselves absolved of all sins. In any case, believing in the work of Christ and turning to God to repent are essential. Peace comes only to the one whose heart is clean and pure.