You have to check if you have the folder with name manager inside the folder webapps in your tomcat.
Rubens-MacBook-Pro:tomcat rfanjul$ ls -la webapps/
total 16
drwxr-xr-x 8 rfanjul staff 272 21 May 12:20 .
drwxr-xr-x 14 rfanjul staff 476 21 May 12:22 ..
-rw-r--r--@ 1 rfanjul staff 6148 21 May 12:20 .DS_Store
drwxr-xr-x 19 rfanjul staff 646 17 Feb 15:13 ROOT
drwxr-xr-x 51 rfanjul staff 1734 17 Feb 15:13 docs
drwxr-xr-x 6 rfanjul staff 204 17 Feb 15:13 examples
drwxr-xr-x 7 rfanjul staff 238 17 Feb 15:13 host-manager
drwxr-xr-x 8 rfanjul staff 272 17 Feb 15:13 manager
After that you will be sure that you have this permmint for you user in the file conf/tomcat-users.xml:
<role rolename="admin-gui"/>
<role rolename="manager-gui"/>
<user username="test" password="test" roles="admin-gui,manager-gui"/>
restart tomcat and stat tomcat again.
sh bin/shutdown.sh
sh bin/startup.sh
I hope that will works fine for you.