Retrieve URL not in HTML page?

The files that you see in the Network Tools area of the browser is a recursive list of all files linked from the HTML page and all of its children.

For example, you load a single HTML page. The page will like to CSS stylesheets. Those stylesheets may include other stylesheets, fonts, background images, etc. The browser retrieves each one of those at its discretion.

The HTML will also likely include one or more JavaScript links, including jQuery, jQuery libraries, Bootstrap or Foundation etc. Each of those scripts is able to tell the browser to retrieve a remote file.

Then even once everything that the HTML and its children link has been loaded, you have AJAX -- additional web server requests based on asynchronously running scripts, or in reaction to user input such as moving the mouse or clicking.

So to get the information you are looking for you would need to implement this recursive fetching and analysis behaviour, which is equivalent to writing a good chunk of a web browser itself. In that case you could look at the source code for Chromium or perhaps a text-based browser like Lynx.

Alternatively perhaps you could write a browser extension, which would likely give you access to the information that you see in the Network Tools panel.

In terms of being able to accomplish this with a small script of a couple of hundred lines of code, I would say it is close to impossible.