Regret is due to a thing done or left undone.
Sorrow is due to some loss or occurrence of evil.
1. In our old age we regret having done many things in the thoughtless days of our youth.
2. I regret that i missed the concert.
3. I regret to inform you that your application for the job was unsuccessful.
1. God is our only comforter in the sorrows of life.
2. The mother's sorrow at the death of her only child knew no bounds.