Repentance is simply a change of mind along with corresponding actions. There is a Godly type of sorrow and an ungodly type of sorrow. Godly sorrow leads to repentance. Ungodly sorrow, or the sorrow of this world, just kills.
Our culture has rejected all "negative" emotions. But God gave us the capacity for these negative emotions, and there is a proper use of them. Ecclesiastes 7:3 says, "Sorrow is better than laughter: for by the sadness of the countenance the heart is made better." People should feel bad about sin. There should be sorrow over our failures. This sorrow should lead to repentance. Then, when forgiveness is received, our sorrow should be cast upon the Lord (Isaiah 53:4).
The Lord's statements to His disciples, the night before His crucifixion, caused them sorrow (Matthew 26:21-22; John 16:6). If they would have let that sorrow lead them to repentance, then they wouldn't have denied the Lord. Peter's sorrow after his denial of Jesus changed him.
The sorrow experienced by those who do not turn to God produces only death. They grieve over their situation because they don't turn to God (that's repentance). Christians should only have sorrow until they repent. Godly sorrow that produces repentance leaves us with no regrets. The positive change that our sorrows led us to, changes our attitude towards the things that caused us sorrow.