When you decide to say sorry, it only makes sense to do so if you do it right. That is, you realize you have completely messed up and you need to apologize big time, but if you do it in a half-hearted fashion, or with conditions attached, then it is absolutely pointless!
I have met people who have said their sorrys even while stressing (ok, perhaps just hinting) that they are still in the right and that they have the complete and full right to mess up, yet are saying the words because it is the expected thing. Back off! You just don't have to say sorry that way. It is useless. It makes no one feel any better. You are still upset because you think the situation is forcing you to apologize and you are not making the other person feel any better since they can always tell your feelings are not genuine! So it is far far better to just shut up, get over the hurt feelings either way and then come back later and say a real sorry that you mean and that comes from your heart. Not one to save your face or just patch up or just because somebody else thinks you should say so.
And mind you, it is not easy to let yourself become so vulnerable and actually be able to get those words out. I think if you can't do it right face to face, it is perhaps an option to show just by your actions that you have realized your mistake and want to make amends. That gives the other persons some time to think too. But whatever the situation, the very minute you realize you are actually in the wrong and you have been able to at least see the other perspectives, you ought to make those amends really quick. Like asap! It makes you feel a whole lot lighter, better, happier :)