What's the meaning of "Sorry"?

So, the World Cup is over, and I see humans everywhere trying best to reclaim their normal routines after a whole month of staying up to catch 3am games and having the next morning completely wrecked.

But I notice debate is still raging over that head-butting incident involving French darling Zidane and Italian (relative) unknown Materazzi.

It has become a "he said-he said" impasse. Materazzi denies insulting Zizou's mother and sister. Zizou said he did. One of them is lying. Whatever it was that was truly said, only the two of them know now.

What really intrigues me is what Zizou said when he met reporters this week - that he is sorry he did the head butt thing, but that he "does not regret" doing it considering what was said of his mom and sister.

That to me, is not a true apology. When one says sorry for something, one expresses regret, right?