The 63-year-old - who will reprise his role as Bobby Ewing - described TNT's update as "a perfect 2012 version of Dallas" but admitted that he is unsure how it will be received.
"If we do it again, there's a chance of screwing it up," he admitted to the Los Angeles Times. "And if this new show fails, the whole world will hear about it."
However, exec producer Cynthia Cidre insisted that the new Dallas will be grounded "in a modern way".
"It's a show about two generations where the stories aren't parallel, they're intertwined," she explained. "They feed off each other, and they depend on each other."
Larry Hagman (JR Ewing) and Linda Gray (Sue Ellen Ewing) will also reprise their roles in TNT's Dallas.
New cast members in the revamp include Josh Henderson (90210), Jesse Metcalfe (Desperate Housewives) and Jordana Brewster (The Fast and the Furious).
The series will premiere on June 13 in the US and will air on Channel 5 in the UK.
> Dallas star Patrick Duffy: 'Young cast are great'
Watch a trailer for the new Dallas below: