The actress, 31, starred as Paxton's daughter in the polygamist HBO drama Big Love

Credit: E. Charbonneau/WireImage

Amanda Seyfried is grieving the sudden loss of her on-screen dad, Bill Paxton.

“He was an amazing and supportive father-figure to me in my early career,” she tells PEOPLE. “Incredibly inspired and full of life at every turn, he made you feel like everything was possible. This is a terrible loss.”

The actress, 31, starred opposite Paxton, who died at the age of 61, in the polygamy HBO drama Big Love from 2006 to 2011.

Other stars have honored the late actor, including Ginnifer Goodwin, who played one of his three wives in Big Love, as well as Jamie Lee Curtis, director James Cameron, Helen Hunt and Bud Cort.

Cort, who starred with Paxton in the 1990 thriller Brain Dead, released a statement to PEOPLE saying he’s “not letting go” of the actor.

The 68-year-old actor met Paxton in the 1970s when the Twister star was parking cars at the Beverly Hills Hotel, according to Cort’s rep. The two became fast friends and their friendship endured.

RELATED VIDEO: ‘Big Love’ Costar Ginnifer Goodwin Reminisces About Bill Paxton

“All of the laughs and joyful times and deep conversations we’ve shared for so many years are safe in my heart forever,” Cort’s statement read. “You really did it and with such style, class and soul and intelligence and, of course, your incomparable humor.”

“It was an honor to be your friend and a privilege to act with you, to make music with you and… most of all, just to hang with you,” he continued. “I love you, Bill. All my prayers and deepest sympathy to Louise, James and Lydia and to your mom and brother and your great dad John, who I know for sure you are with now. God bless you brother.”

Paxton died due to complications from surgery. His fame rose in the 1990s thanks to roles such as Morgan Earp in Tombstone(1993), Fred Haise in Apollo 13 (1995), the lead role in the 1996 hit Twister and as treasure hunter Brock Lovett in Titanic (1997).