Paul wrote a letter that caused sorrow, but he said he did not regret what he had done. “I do not regret it … I see that my letter hurt you, but only for a little while. Yet now I am happy, not because you were made sorry, but because your sorrow led you to repentance.” He then added: “For you became sorrowful as God intended and so were not harmed in any way … Godly sorrow brings repentance that leads to salvation and leaves no regret, but worldly sorrow brings death.” (2 Cor 7:8-10)
Being sorry that we have sinned is what brings us to resolve to change our way of life. A changed life is the fruit, the result, of a changed heart or mind. If a person is sorry for his sin, and yet has no desire to change, scripture calls this the “sorrow of the world” which brings punishment and death.
When Paul and others preached repentance and baptism so sinners could be saved, like John the Baptist had also preached, some wanted to hear more, but others “were filled with jealousy and spoke abusively showing themselves to be unworthy of eternal life.” (Acts 13) Some had no heart of repentance, but picked up stones and tried to kill him.
A man who has done the right thing has no reason to repent of it. Paul courageously rebuked Peter when Peter sinned (Gal 3). Paul did the right thing and had no remorse or regret in so doing.