What you receive when you deploy a Droplet differs drastically than what you receive with cPanel. A Droplet is either a base OS (Operating System) image or whatever is provided with the one-click that you deploy. Other than the DigitalOcean CP, there’s not a control panel and everything is managed from the CLI (Command Line Interface) using Terminal, PuTTy, or your preferred method.
With the base OS, you’re responsible for setting up Apache or NGINX as your web server as well as installing any additional software that you may need (i.e. PHP, MySQL, NodeJS, etc).
The one-click images provided by DigitalOcean will allow you to jumpstart things a little quicker by providing an image that has most of these things installed for you, though they do not provide a mail server.
If you need a mail server, such as what is provided by web hosting providers that use cPanel, you’d need to install, configure, and test this on your own.
You could use something such as MailCow, which will automate the setup an a fully functional and working e-mail server, though it’s advised that this is setup on a Droplet that is separate from the one you would use for actual hosting of your content.
You can check out the MailCow project here:
I’ve used it in the past and it works well, though as with anything e-mail related, mail servers take time to run, update, upgrade, etc. It’s not as simple as deploy and leave it alone – the above will, however, get you off to a jumpstart and it does install all the bits and pieces needed for fully functional e-mail.