I have set up tomcat 8 according to this, and I have the following tomcat-users.xml file:
In my case it was the security constraints defined in web.xml. Make sure they have the same roles you use in your tomcat-users.xml file.
For example, this is one of the out-of-the-box tags and will work with the standard tomcat-users.xml.
HTML Manager interface (for humans)
/html/*
manager-gui
In my case an admin had used a different role-name which prevented me from accessing the manager.