“I’m sorry you feel that way” isn’t an apology. It’s a return label sending the problem back to them.

An apology that relocates the problem to the other person is not an apology, and everyone hears the difference immediately. The words perform regret while the substance denies any part in it, which usually leaves the other person worse off than silence would have. The instinct behind it is self-protection rather than cruelty, and the effect is the same either way.

Say what you did, without the word if. Name the specific action, acknowledge the effect, and stop talking before the explanation arrives, since the explanation is what undoes it.