"In the final game of the 2006 World Cup, French midfielder Zinedine Zidane headbutted Italian defender Marco Materazzi for insulting him. In the aftermath, Zidane apologized in an interview with a French television station but added that he didn't regret his actions. Can one coherently apologize for an action yet not regret the action?
An apology is an acknowledgment of responsibility and an expression of regret. However, the words "I'm sorry" are not always meant to convey an apology. When I tell a friend who has recently lost a close relative that I'm sorry for his loss, I 'm not accepting responsibility or expressing regret for anything I've done. I'm merely expressing my feelings of sympathy. So whether Zidane was inconsistent depends on precisely what he said. It would be perfectly consistent for Zidane to express sympathy with the French people for what happened but deny that he regrets his actions.
Of course, the problem with this is that most of us feel that Zidane should do more than say "I'm sorry" out of sympathy. He did something wrong, and he should say "I'm sorry" out of regret. He should, in other words, apologize.
Let's see what he did say. According to the BBC's translation, it went like this: "It was inexcusable. I apologize. But I can't regret what I did because it would mean that he was right to say all that." If that's an accurate translation, then clearly Zidane's apology was insincere. His proviso ("But I can't regret what I did") pretty much ensured that the apology would not be taken seriously. And so, to answer your question, if the BBC translation is a good one, then there is something problematic about what Zidane said. It is inconsistent to say: "I apologize for what I did, but I don't regret what I did."
While we're on the subject, there's something else puzzling about Zidane's comment. He says that he can't regret his action "because it would mean that he [Materazzi] was right to say all that." But it doesn't mean that at all. If someone is saying inappropriate things to me (on or off the pitch), I do not acknowledge that he is right to say them by refusing to respond violently!