If it's on the same machine, you can simply use "localhost" as the network name, that always translates as "this machine" in all the networking code ever. No need to check the IP addresses.
So your webadmin should work at http://localhost:8080 and minecraft should be perfectly happy with the address "localhost" (add the port if not standard)
So your webadmin should work at http://localhost:8080 and minecraft should be perfectly happy with the address "localhost" (add the port if not standard)