One who is embarrassed by a sin shows that he is actually detached from his action, even as he does it. The root of Teshuvah is admission and confession of his sin, which brings G-d to accept his repentance. The concept of admitting means giving myself over, submission, to the person who has a claim against me. To admit to G-d that we have sinned is an admission that we have not lived up to our potential or our responsibilities. To do this requires an intellectual recognition of G-d, our responsibilities toward Him, and our true relationship to Him.
Sins simply increase that distance.
The possibility of return, of getting closer to the Divine source of our existence, is the result of G-d's mercy, giving man an opportunity to transcend the limitations imposed upon him by the creation process. From the above, we learn that Teshuva really means coming closer to the source of our existence, after having been distanced from it. This is why prayer is the essence of service, as it demonstrates man's complete dependence on and subjugation to G-d. With physical sacrifices, we give our possessions over to G-d. A closeness is forged.