How can I manage facebook comments under my articles on joomla site?

You can't delete a user's Likes, but you can remove comments that aren't wanted. If you're logged into Facebook with the administrator account for the application you're using within JFBConnect, in each comment, there should be a "Moderate" link where you can delete the comments. This doesn't always show, in which case, you can use Facebook Moderation Page, which will show you all comments on all pages of your site (pretty handy):
developers.facebook.com/tools/comments

Hope that helps,
Alex