Hagman had famously tipped Damon to play the son of JR Ewing in TNT's Dallas when casting was still underway. The role ultimately went to Josh Henderson.
Damon has now told ET Online that he had tremendous respect for Hagman, who died from cancer complications at the weekend.
"I grew up watching him. 'Who Shot JR?' was more than a TV event. It made its way into my consciousness at a very young age," he explained to the news service.
Damon further commented: "I was probably 10 or 11 when all that was going on. He was certainly impactful in a way that is probably much harder to be now.
"There's a lot more channels and a lot more noise. He's a huge part of American culture."
Hagman's former co-stars Barbara Eden, Patrick Duffy and Josh Henderson have also shared their favourite memories of the actor in recent days.
There will be private and public memorial services for Hagman in Texas and California later in the week.
> Larry Hagman's career: Dallas, I Dream Of Jeannie - video
Photo Gallery - Larry Hagman 1931 - 2012: