Forget the politics, forget trying to explain what you were trying to say--you always make matters worse if you wait. Or, as in this case, you try to soften the blow by saying "I'm sorry you misunderstood" or "I apologize if I've offended anyone." That's not saying you're sorry...that's saying that anyone who was hurt by your statement is either dense or thin-skinned.
There are actual theories about the use of apology, by Kenneth Burke and Ware and Linkuegel, that list a number of rhetorical options ranging from denial to transcendence. That's fine when you're giving a Socratic reposnse to specific charges. But 21st century politics and 24-hour media cycles have changed the rules. There's talk radio and faux cable news anchors and bloggers to keep the pressure on. Today, transcendence fails, transparency perserveres.
As a media consultant, I advise my clients to face the press immediately when it becomes clear that something they said has caused a kerfuffle. "I made a mistake. I shouldn't have said it. I'm sorry." There. Pretty simple. It shows respect and humility--things we all could use a little more of.