Hacking around I found a way to solve the above issue and that can give you a freedom from plugins and hefty set-ups to automate WordPress article posting to Facebook and Twitter page/account. Here is the way:
- Have your Google Feedburner account. Link
- Connect your wordpress site/blog with Twitter account. Read this..
- Then connect your Twitter account with Facebook. Just complete the set-up by Settings -> Profile -> Facebook . This will auto-post to your Facebook account.