For some reason Magento changes the file permissions of the
index.php file when you upgrade Magento. It does not happen on
every server but on many it does. The file permissions change
to 666 and it should be 644. So login to the root of your
Magento and change it back.

Magento Downloader not working after upgrade to 1.9.2

The same problem also happens to the Magento downloader folder.
So go to that folder and change index.php from 666 to 644.