Regret is not a proactive feeling. It is situated in disappointment, sorrow, even remorse. It merely wishes things were different without an act to cause a difference. However, repentance is different. Repentance is an admission of, hatred of, and turning away from sin before God.
Repentance allows God's mercy to come forth because it recognizes that the sin committed was against God. It also bares contriteness of the heart and the desire to walk in the Spirit and not in the flesh so that particular sin will never be repeated.
It's only through Christ that we can take full advantage of God's mercy and forgiveness through repentance in Jesus' name.