Do you use a Facebook application ID? If you do, you should see a link under the comments box plug-in where you can administrate/moderate comments. I think there is an option there for you to ask to be notified of comments; I'm not sure about this because I haven't got as far as trying it out yet (because of what I say in the next paragraph) but it looks like that is what it does. You can get an app ID from here
I should warn you first, though, at this point I am having a problem with my comments plug-in — I previously did not use an app ID and people left comments on my website without problem. After I got an app ID and started using it, all the previous comments have disappeared. Also, if I try to go back to not using an app ID the comments box will no longer load. I say this to you because I don't want you to start using an app ID and lose all your comments on your website
I am currently trying to find out if it is a "feature" of the Facebook platform (or the Drupal extension module I am using) or a bug. Please feel free to follow along with my question on this forum which will hopefully clarify the issue.