Facebook API Post Search Deprecated?
As mentioned Niraj Shah, searching by the type "post" is already 'Legacy' API method and could be used with path '/v1.0/search?type=post', BUT there is one more trouble - your application can't use v1.0 API, if it was created after 30th April 2014. So be careful. According this answer.
UPDATE
Graph API v1.0 has been fully deprecated and is no longer available as a workaround. Original answer below for reference.
Yes, version 2.0 of the GraphAPI does not let you search for posts anymore. See the updated documentation.
You can continue to search for posts by changing your API call to:
https://graph.facebook.com/v1.0/search?q=search_query&type=post&access_token={access_token}
I.e. add v1.0/ after https://graph.facebook.com/
According to Facebook, "All Facebook-enabled apps will be automatically upgraded to API v2.0 on April 30, 2015. If you have mobile apps, you'll need to update your app well before that date - leaving additional weeks for people to download your update from the store", and "Public post search is no longer available".
Check this for details: https://developers.facebook.com/docs/apps/upgrading