After a two-week flap, David Letterman finally and directly apologized to Alaskan Gov. Sarah Palin and her daughters on his program last Monday night, saying he wanted to say he was sorry “to the two daughters involved, Bristol and Willow, and also to the governor and her family and everyone else who was outraged by the joke.”

In case you’re like me and can’t stay up for the late show, two weeks ago, Letterman joked about Gov. Palin attending a Yankees game with her daughter. The joke, in which Letterman seemingly confused Willow, who is 14 and attended a Yankees game that week, with Bristol, who is 18 and an unwed mother, had to do with Palin’s biggest problem being keeping her daughter from being “knocked up” by Yankees slugger Alex Rodriguez.

I agreed with Palin and others who thought the joke inapropriate and that it contributed to the unhealthy sexualization of young girls. Letterman initially attempted to apologize by saying he meant Bristol, not Willow, seeming to imply that Bristol was fair game since she was 18 or an unwed mother or some such nonsense.

That apology did not go far enough and, I would argue, that the current one doesn’t either. My problem lies with Letterman apologizing to “anyone else who was outraged.” This is common language – from the famous Howard Stern apology on down – to apologize to “those who were offended or outraged.”

This wimpy wording seems to imply that people who are offended or outraged have the problem, as opposed to those who made the comments in the first place.

What’s the right way to apologize when you’ve said something inappropriate in the workplace? Be a man or a woman about it and take the blame squarely. Say: What I said was wrong. I shouldn’t have said it. I’m sorry. What can I do to make it up to you?

In the workplace, of course, with all the complexity of diversity issues these days — as I wrote in my book Stop Pissing Me Off  it’s easy to make mistakes. When you do, the right thing to do is to apologize. The right way. The first time. Don’t wimp out. Don’t imply that they have the problem for being offended.

And if you really mess up, grovel.

If you’re on the other side, accept the apology, as did Sarah Palin. Be gracious. Workplace diversity is complex these days, and we’re all learning. We need to be humble, do your best and move on.

Even those of us who are very experienced make diversity mistakes. I remember a big one that I made. I was asked, along with three other diversity consultants, to conduct diversity training for a very prestigious East Coast medical school. This was going to be a big deal since they were going to take the doctors out of the hospital and the university for three days to sit through this training.

Among the four of us consultants, we probably had about a hundred years worth of experience in doing diversity work so we thought we were pretty hot stuff.

We had never met the HR vice president who hired us. We conducted the entire pre-work by phone or email. We designed the program to be interactive, with the students dashing around in the training room and roaming outside.

When we arrived the first day, we marched into the training room to meet the VP. Guess what? She’s in a wheelchair!

We had never thought to ask whether anyone would need any kind of accommodation to do all the exercises. All of us wanted to sink through the floor.

Of course we apologized, scrambled and accommodated her into the program. Luckily, she was gracious about our error.

We all walk through the world with blinders on, limited by our own personal history and culture. If we waltz into a room, we don’t think about those who wheel in. What works is not to deny that we have these limitations, but to constantly strive to learn, to uncover them and to ask respectful questions.

And when we do mess up, of course, we apologize. David Letterman – not.