I don't like "I'm sorry you feel that way." The person is trying to count this as an apology, but it is totally not an apology. Instead, it shifts the blame to the other person by saying that the problem is not the offense that the first person committed, but rather is that the other person did not care for being the victim of the offense. This phrase says that if the other person would just stop feeling that way, then there would be no problem, even though in reality the other person's feeling is appropriate for the occasion.
Example: An employee complains about sexual harassment in the workplace, explaining why the perpetrator's actions are creepy and need to stop. When the perpetrator is called out on this and the victim explains how what he is doing makes her skin crawl, he responds "I'm sorry you feel that way" and expects the problem to go away without him having to own up to his behavior.