F1 announced last month that Carey would be stepping down as CEO and chairman at the end of the year, handing the reins over to ex-Ferrari team principal Domenicali.
Carey will remain with F1 as a non-executive chairman, assisting the transition to Domenicali upon the Italian's formal start date of 1 January.
Speaking on the Beyond the Grid podcast, Carey said F1 went through an extensive process to find his replacement before settling on Domenicali.
"We went through a very broad search, looking at a complete range from A to Z of candidates," Carey said.
"I came into this as an outsider, and I think there was some value in coming into the sport as an outsider, because I felt it needed significant change and fresh perspectives, a different set of perspectives.
"Going forward now, what we felt was right, we wanted somebody who can maintain the momentum and continue to build on what we think we've put in place to grow the sport.
"One of the important things Stefano brings is a deep knowledge of not just the sport and the competition on-track, but the players in the sport, and therefore I think he can hit the ground running in terms of taking things forward."
Domenicali spent more than 20 years with Ferrari, serving as the team principal of its F1 operation between 2008 and 2014. He later went on to hold roles at Audi and Lamborghini, as well as being the president of the FIA's single-seater commission.
Domenicali's appointment has won widespread praise throughout the paddock, with Carey echoing the belief of many that his personality makes him well-suited to the role.
"Stefano brings a unique personalty to this, somebody that has great respect," Carey said.
"Sometimes I feel that this role you're sitting in the eye of a storm, with a lot of partners circling around. I think he brings a balance, and an even-keeled personality to navigate through what at times can be a very noisy situation.
"I think the combination of unique expertise and experience with a personality that can navigate through the various dynamics that exist make him ideally suited for this."
Mercedes team boss Toto Wolff revealed that he held some initial talks with F1 about taking over from Carey, but they ultimately "never went anywhere" amid opposition from rival teams.
Carey refused to be drawn on F1's consideration of Wolff for the role, saying that the only offer made was to Domenicali.
"I'm not going to get into who we talked to or considered," Carey said. "We went through a search of looking at a range of people across the board.
"I'm really not going to comment on and don't think it's appropriate to comment on who we considered. We only made one offer, and that offer was to Stefano, and we're thrilled to have him in place."