UPDATE: This solution is no longer valid. FQLs are deprecated since August 7th, 2016.
https://api.facebook.com/method/fql.query?query=select%20%20like_count%20from%20link_stat%20where%20url=%22http://www.techlila.com%22
Also http://api.facebook.com/restserver.php?method=links.getStats&urls=http://www.techlila.com will show you all the data like ‘Share Count’, ‘Like Count’ and ‘Comment Count’ and total of all these.
Change the URL (i.e. http://www.techlila.com) as per your need.
This is the correct URL, I’m getting right results.
EDIT (May 2017): as of v2.9 you can make a graph API call where ID is the URL and select the ‘engagement’ field, below is a link with the example from the graph explorer.
https://developers.facebook.com/tools/explorer/?method=GET&path=%3Fid%3Dhttp%3A%2F%2Fcomunidade.edp.pt%26fields%3Dengagement&version=v2.9