As also mentioned, there needs to be some regret - acknowledgement of something that needs correcting - to repent and improve, as God intends.
This realization of better ways is part of the gospel - "good news.".
I don't mean to keep harping on this, but this view conflicts with Paul's statement regarding the difference between mere regret -- which is self-centered -- vs. Godly sorrow leading to repentance.
2 Corinthians 7
8 For though I caused you sorrow by my letter [the epistle we call 1 Coritnhians], I do not regret it; though I did regret it -- for I see that that letter caused you sorrow, though only for a while --
9 I now rejoice, not that you were made sorrowful, but that you were made sorrowful to the point of repentance; for you were made sorrowful according to the will of God, so that you might not suffer loss in anything through us.
10 For the sorrow that is according to the will of God produces a repentance without regret, leading to salvation, but the sorrow of the world produces death. [Emphasis added]
We see in that sentence the difference between regret and Godly sorrow that leads to repentance. Paul felt regret -- the Greek
metamellomai -- that he had caused sorrow, but he did not repent -- the Greek
metanoeo -- of it. Paul did not repent, feeling only regret, because he knew the members of the church at Corinth needed to hear the message he sent. But the Corinthians did repent, having heard Paul's words are realized how off track they were. They felt the Godly sorrow necessary to truly turn away from their sin and move in a new direction.
Regret is strictly within ourselves and leads to nothing beyond uncomfortable feelings. Judas regretted his act of betraying Christ. He did not repent -- the word
metanoeo is not used in reference to Judas. He felt only regret that his plot failed to force Jesus to declare His kingdom rather than die on the cross. Judas truly was clueless. Only when we are truly moved by the Spirit of God within us do we feel the sorrow of what we have done -- not sorrow that we've been caught, or failed, but sorrow that we have offended God and others and damaged the fellowship we have with Him and them.
We feel regret all the time, but we keep it to ourselves. We do nothing with it. Regret is useless, because it causes us to keep our sins bottled up inside of us, not confessing them to God or anyone else. Only when we begin to feel sorrow and a need to confess, as well as a need to repent -- turn around, "about face" as the Greek
metanoeo is literally translated -- that we get outside of ourselves and take the steps we have known all along we need to take but have not.
You can call what you feel "regret" if you wish. But in the strict context of the Bible, simple regret is self-centered and leads to nothing.