Spotify currently boasts 170 million monthly active users, of which 75 million are paid subscribers. Apple Music recently crossed 40 million paid monthly subscribers.
Cook's comments mirror Apple's longstanding criticism of the way Spotify suggests music and builds playlists for its users.
A popular feature of music streaming platforms is the public playlists they create based around moods, genres and more.
Most build these via complex algorithms that combine the listening histories and personal playlists of thousands of different users.
Apple Music, which boasts around 50 million users to Spotify's 170 million, prefers to uses human curators to create playlists.
Speaking to Fast Company, Cook said the company was making a conscious attempt to bring a human touch to its playlists.
He said: "We worry about the humanity being drained out of music, about it becoming a bits-and-bytes kind of world instead of the art and craft."
Apple Music is locked in a fierce battle with Spotify to take the crown as the world's number one music streaming site.
Apple has a lot of catching up to do: It has a combined 50 million paid and free trial listeners while Spotify has 75 million paying customers alone.
But the Cupertino firm is quickly making ground on its biggest rival considering Apple Music launched just three years ago.
Apple also has an edge on its rivals in that its status as the world's most valuable company means it has not needed to worry about profitability.
"We're not in it for the money," Cook told fast Company.
The rise of music streaming services has provided a huge boost for the music industry, turning listeners away from illegal downloads, which crippled the industry throughout the late 90s and mid-2000s.
According to figures published last week by YouGov, just one in 10 Britons now get their music from an illegitimate source – down from 18 per cent five years earlier.
Of those who still download their tracks illegally, more than a fifth (22 per cent) claim they will likely move to a streaming source within the next five years.
Researchers said the statistics showed "encouraging signs" that streaming services could one-day eradicate online music piracy.