I did a bit more research and seem to have used better key words because I found my solution now. I wanted to share the solution with everyone, in case someone else may ever need it.
Create folder for configuring docker service through systemd
Create service configuration file at /etc/systemd/system/docker.service.d/http-proxy.conf and put the following in the newly created file
# NO_PROXY is optional and can be removed if not needed
# Change proxy_url to your proxy IP or FQDN and proxy_port to your proxy port
# For Proxy server which require username and password authentication, just add the proper username and password to the URL. (see example below)
# Example without authentication
# Example with authentication
Reload systemctl so that new settings are read
sudo systemctl daemon-reload
Verify that docker service Environment is properly set
sudo systemctl show docker --property Environment
Restart docker service so that it uses updated Environment settings
sudo systemctl restart docker
Now you can execute the docker-compose command on your machine without getting any connection refused error messages.