Mr Cook said internet users had the right to expect privacy when using different services online, and Apple was responding to that.
Facebook, along with other internet companies, has been accused of excessively collecting personal data from users, in many cases as a way to better serve adverts.
At its developer conference on Monday, Apple unveiled Sign In With Apple, a new online tool that will enable users to log in to apps and websites using their encrypted Apple ID, rather than having to share their credentials from social sites.
Speaking to US broadcaster CBS, Mr Cook said the tool was not designed to be a criticism of others.
“We’re not really taking a shot at anybody, we focus on the user,” he said.
“And the user wants the ability to go across numerous properties on the web without being under surveillance.
“We’re moving privacy protections forward and I actually think it’s a very reasonable request for people to make.”
The Apple chief executive added that he thought heightened awareness of online privacy was good for democracy, as well as technology companies.
“I think that everybody is beginning to care more. People are becoming more aware of what’s been happening. Many people are getting more offended – this is good – because we need to shine a light on it,” he said.
“You can imagine an environment where everyone begins to think there’s no privacy, and if there’s no privacy, your freedom of expression just plummets because now you’re going to be thinking about that everybody’s going to know every single thing that you’re doing.
“This is not good for our country. This is not good for democracy.”
The tech giant’s Worldwide Developer Conference (WWDC) also saw Apple confirm it was to replace iTunes with three apps – Music, TV and Podcasts – after 18 years of running the service.
The iTunes Music Store will still be used to purchase music, but rather than appearing as a standalone app on Mac computers, it will form part of the restructured Music app. Other iTunes features will also be integrated into the TV and Podcasts apps.
The service will remain unchanged on Windows.
New dedicated software for the iPad – called iPadOS – was also announced, alongside the next version of iOS, iOS 13, which will include a dark mode for the first time, for use in low-light conditions.