The word for sorry, da-ag, does not refer to feeling bad about one sins, but carries the connotation of acknowledgment and accepting responsibility for what you have done.
Confession of sins, is taught in the fourth and fifth sacrifices, which are spelled out in Leviticus chapters four and five respectively, and further described in 1 John 1:9.
When a person has sinned, if they are a believer in Christ, then they place themselves outside of a functioning relationship with God. They are still saved, but their relationship is off-line, so to speak.
One of the fundamental principles of Christianity, is that a functional relationship with God, only occurs while a person is in fellowship.
Confession restores your fellowship, so that your relationship functions as it should.
An unbeliever, has no relationship with God, and therefore, confession has no effect.
Once a person is saved, by believing in Christ, then the issue becomes whether or not they will live their life while residing in fellowship, or out of fellowship.
Sin and confession, are the key elements that determine whether you are in fellowship or out of fellowship.
That is, when you commit a sin, you are immediately out of fellowship. When you confess your sins, then you are immediately restored back into fellowship.
Because most people do not follow the confession principle on a daily basis, they will live the bulk of their life out of fellowship, and therefore do not have a functional spiritual life.
All spiritual activity, functions only when you are in fellowship.
And as stated within this verse, confession is mandatory, and your attitude that accompanies confession, is your acknowledgment and acceptance of the things that you have thought, or said, or done.