Speaking in his first live media interview since stepping into Apple's top job, Cook said that he was not trying to be the next Steve Jobs, Apple's co-founder who passed away last year.
"Steve was a visionary," Cook said. "My role was never to replace him."
Later, he added: "I learned a lot from Steve. It was absolutely the saddest day of my life when he passed away."
During a discussion with journalists Kara Swisher and Walt Mossberg at D: All Things Digital, Cook did not reveal any specifics on forthcoming Apple initiatives, and said that the firm would "double down on secrecy on products".
But after Mossberg noted that Jobs had talked in his final media appearances about wanting to change TV, Cook said that the main living room screen remains "an area of intense interest for us".
Referring to previous comments made by both Jobs and himself that the Apple TV set top box product was "just a hobby", Cook said: "We're not a hobby kind of company, as you know. We've stuck in this."
He added: "It's not a fifth leg of the stool. [But] it's not of the same market size as the phone business or the Mac business or the music business or the tablet business."
Cook said that the Apple TV sold 2.8m units last year, but has shifted nearly that many in just the first few months of 2012.
"This is an area of intense interest for us," Cook said of the TV service. "We are going to keep pulling the string and see where this takes us."
The Apple boss did not discuss the rumors, but did "agree" that the current Apple TV product was not enough to solve all the current problems in the TV industry.
"We would look not just at this area, but other areas, and ask, can we control the key technology?" said Cook.
"Can we make a significant contribution far beyond what others have done in this area? Can we make a product that we all want?…Those are all the things we would ask about any new product category."
There have been previous suggestions that Apple has struggled to launch a more ambitious TV product due to its fractious relationships with the Hollywood studios and TV networks.
But Cook said: "We have very good relationships with the content owners. We don't want their stuff to be ripped off."
He added that Apple should not aim to become a "content business" (seemingly ruling out a major acquisition), but instead look to partner with the existing players to offer services to consumers.
"I don't think Apple has to own a content business," Cook said. "We haven't had an issue, for the most part, getting content. This is an area where Apple partnering well is the right approach."
Cook said that he was "loving every minute" of being Apple chief executive, and revealed that he was amazed by all the "the things I cannot talk about today".
He added: "The juices are flowing, and we have some incredible things coming out."
Cook discussed the great reception that the iPad was getting from people of all ages and backgrounds since its launch in 2010, but added that "it's just the first inning. It's only been two years."
Asked what may be the second innings for the tablet, Cook replied coyly: "That's a great question. I'm not going to answer it."