Error 404 using RewriteRule in .htaccess

I am currently improving the usability of a website through friendly URLs. I have done this several times and what I typically do is hide the *.php or *.html extension using .htaccess following this code:

RewriteEngine On

RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^([^\.]+)$ $1.html [NC,L]

However, this code seems to resist to work in the server this website in hosted in. I am getting a 404 not found error if I try to access without the extension added.

http://ift.tt/1KPIip3

http://ift.tt/1zGzSiB

Any ideas of how to fix this problem?