The flip side is true--for the most part you don't want to apologize for not writing.
I'm not saying that if your angry Aunt Mabel confronts you about not sending a thank you note for the wedding gift she sent, that you shouldn't apologize. And if you promised someone a book chapter by a certain date, you also should apologize if you don't make the deadline.
But to the extent that you may be failing to get work done because you're suffering from writer's block? That's nothing to apologize for. In fact, apologizing for not writing may make it more difficult to write--if feeling bad about not writing today makes you feel like there's more pressure to write tomorrow, and feeling bad about not writing yesterday puts more pressure on your to write today, then that emotional tension can interfere with writing.
Writer's block is a common problem and one that can be overcome by practice. If you haven't been writing and you want to be writing, don't worry about what you haven't written, just try to put your ideas down on the page and see what you can write. And if what you can write is imperfect--well, you don't need to apologize for that either.