Kevin Costner is remembering his Dances with Wolves costar Graham Greene after his death.

On Tuesday, Sept. 2, one day after the Canadian actor’s agent confirmed his death at 73, Costner shared a tribute to his late colleague on social media.

“A few things come to mind when I think of Graham Greene and our time together on Dances With Wolves,” Costner, 73, began on Instagram.

His post featured a clip from the 1990 Western about a Civil War soldier who develops a relationship with a band of Lakota Indians. In the clip, Costner’s character, Lieutenant Dunbar, attempted to have a conversation with Greene, who portrayed Kicking Bird (Ziŋtká Nagwáka), and his tribe.

Despite their language barrier, Costner did his best to talk to the tribe about buffalo, acting out how the animal would behave.

Costner recalled “how willing” Greene “was to learn the Lakota language.”

“I think of my joy when I heard that his work on the film was recognized with an @theacademy Awards nomination,” the Yellowstone star wrote of his directorial debut. “And I think of this scene in particular, when he was able to establish so much about the relationship between Dunbar and the natives with so few words.”

Greene earned an Oscar nomination for Best Supporting Actor for his role.

In his tribute, Costner remembered Greene as someone who “was a master at work and a wonderful human being.”

“I’m grateful to have been witness to this part of his lasting legacy. Rest in peace, Graham,” he concluded.

Greene died on Monday, Sept. 1, “after a lengthy illness,” his agent told PEOPLE.

In a 2017 interview with Reader’s Digest Canada, Greene said he kind of “stumbled into” acting after starting out “as a carpenter, a welder, a draftsman, a carpet layer, a roadie and an audio tech.”

What he loved most about acting was that “These people keep me in the shade, give me food and water, take me over to where I say what I’m supposed to say, then they take me back.”

He compared the seemingly easygoing lifestyle to that of a dog.

In addition to Dances with Wolves, Greene’s work includes 1994’s Maverick, 1995’s Die Hard With a Vengeance, 1999’s The Green Mile, 2009’s The Twilight Saga: New Moon, and 2012’s The Twilight Saga: Breaking Dawn – Part 2, as well as several television roles.

He is survived by his wife Hilary Blackmore, daughter Lilly Lazare-Greene and grandson Tarlo.