"You've got to be willing to be a hero in order to take on that job," he told CNN at the film's premiere Tuesday night.
It's been seven years since Sullenberger and his co-pilot, Jeff Skiles, made an emergency water landing after hitting a flock of geese, but Sullenberger is just starting to get used to all the attention.
"I certainly have begun to have a better a understanding of why people feel that way about the story and about me," he told CNN. "So I've decided to not take that label on as my own but to graciously accept that when it's offered to me and I also understand that this entire film is really a story that no one knows."
The landing was hailed as "The Miracle On The Hudson" by the media when all 155 passengers survived, but behind the scenes, Sullenberger was under investigation by the Federal Aviation Administration and the National Transportation Safety Board.
"This entire film is really a story that no one knows," Sullenberger said. "It's what happened after we landed ... and the investigation had to take place to make sure we did everything right and for many months we didn't know the evidence would eventually exonerate us, which it did. But it still didn't make it any easier during a troubling time in the interim."
Sullenberger, who suffered from PTSD after the traumatic event, admitted that "it was a very emotional experience" to watch the film for the first time with his family.
The film's director, Clint Eastwood, told CNN that he was motivated to tell this story because, unlike so many tragic events, this one had a "happy ending."
"It was a good story ... a very good time for New York when New York was going through a depressed period and post 9/11 ... I think it's important to have some good news once in a while."
Hanks hopes this story will remind viewers to have "faith in our institutions."
"There's a social contract that goes on with buying a ticket and getting on a plane and everything is supposed to work," Hanks told CNN. "In this age where an awful lot of cynicism, a lot of people can second guess what goes on, it all worked the way it was supposed to because the social contract says when it all hits the fan there's one guy who has to get us there and that was Captain Sully Sullenberger."
Eastwood said it was a no-brainer casting Hanks. "Tom is a terrific actor and I had never worked with him," he said. "And I think he's got the same quiet presence that Sully has ... I never went beyond [Hanks] because he accepted, I didn't give it a second thought."
"Sully" opens in theaters this Friday.