The three-part series - which charts the famed Hatfield / McCoy feud of the late 1800s - premieres in the UK on Thursday, October 25 at 9pm on Channel 5.
"McCoy and Hatfield - while they were very different men - they were friends, and they tolerated each other," Costner explained.
The Oscar-winner - who was named 'Outstanding Lead Actor in a Miniseries or a Movie' at this year's Emmys - plays William Anderson 'Devil Anse' Hatfield, with Bill Paxton cast as Randolph 'Randall' McCoy.
"If you talk to Bill, he says his character was very, very opinionated... but he probably deep-down liked McCoy," said Costner.
> Kevin Costner's Hatfields & McCoys breaks own ratings record
> Kevin Costner's Hatfields & McCoys to air on Channel 5 in the UK