I'm confused as to what's wrong.
You went to Netflix.com and downloaded / installed but no icon showed up? Or your watching directly from Netflix? Do you have a shortcut with no icon on your desktop? Or you have no shortcut at all?
What OS are you using?
Below is for Windows XP / 7
To fix you have short cut with no icon you can follow steps below or download it again and re-install
Open Internet Explorer or any web browser and go to http://findicons.com/search/netflix
. Click the image you wish to use and download the ico version.
Right click the shortcut to Netflix on your desktop and click change icon. Browse to the ico file you saved.
There are other icon sites out there. This is the first one I found that SEEMED safe to use, but I do not own the site.
To fix your watching directly from Netflix with no shortcut or icon.
Right click on your desktop and click create shortcut
copy and past this https://www.netflix.com/Login?locale=en-US
name it Netflix.
If I got your needs all wrong please explain more.