The Inbox Counter isn’t compatible with the new 2015 Inbox (https://twitter.com/asana/status/588422761330032640). However, I have a userscript that adds an orange dot to the Asana browser tab favicon when I have unread items in the Inbox.
The way to use my userscript is to go to follow the instructions at https://greasyfork.org. After you’ve installed the browser extension of your choice, search for my script, which is called Asana Dynamic Favicon. Install, and you’re good to go.