How important is regret in the process of repentance?

Our Gemara on Amud Aleph quotes the verse in Bamidbar (5:7)

דַּבֵּר֮ אֶל־בְּנֵ֣י יִשְׂרָאֵל֒ אִ֣ישׁ אֽוֹ־אִשָּׁ֗ה כִּ֤י יַעֲשׂוּ֙ מִכׇּל־חַטֹּ֣את הָֽאָדָ֔ם לִמְעֹ֥ל מַ֖עַל בַּה׳ וְאָֽשְׁמָ֖ה הַנֶּ֥פֶשׁ הַהִֽוא׃

Speak to the Israelites: When men or women individually commit any wrong toward a fellow human being, thus breaking faith with Hashem, and they realize their guilt.

Yismach Moshe (Naso 2) notes that the verse emphasizes confession but omits mention of a key component of Teshuva, regret (charata. See Rambam Laws of Repentance 2:2-3). Yismach Moshe explains, if you do not regret the sin, a “commandment” cannot make you regret it. It seems that the Mitzvah of Teshuva contains a commandment to do confession, however the essential prerequisite is regret. 

This is similar to the opinion amongst Rishonim that belief in God is not one of the 613 mitzvos because it is a prerequisite. Belief in God canny he a mitzvah, instead it is the foundation for the obligation in mitzvos. (See Ramban Sefer Hamitzvos, Aseh 1.) This also is in line with how the Torah stresses practical aspects of observance which focuses its commands on external behaviors. The Chinuch (16) explains this is not because the inner aspects of the heart are unimportant, rather the Torah understands that human nature requires external action to motivate and develop internal states.  

This idea requires mindful application.  Too much emphasis on externality will lead to hollow observance, but too much focus on internality leads to impractical belly-button gazing.  As humans are a hybrid between body and soul, observance must constantly balance the internal and the external aspects of experience.