The actor, who starred alongside Whitney in the 1992 film The Bodyguard, said that he regrets not being able to save the late singer as he did in the film.
"I let her down. I should have been there, and I wasn't," he said. "And now for the rest of my life I will have to live with that pain. I saved her then, I should have saved her now.
"She was my one true love. I still have 'I Will Always Love You' as my ringtone, and I count it a badge of honour every time I get mocked for it."
Costner is expected to speak at Whitney's funeral service in Newark, New Jersey today (February 18).
Clive Davis will also pay tribute to the singer, while Aretha Franklin and Stevie Wonder are tipped to perform.
Alicia Keys and Tyler Perry will both be in attendance at the service, which is being streamed live on the internet and a number of TV channels.
Whitney died last Saturday (February 11) at the age of 48 in her Los Angeles hotel room.
More Whitney Houston coverage:
> Whitney Houston family attend private viewing ahead of funeral
> Whitney Houston 1963-2012: Reactions
> Whitney Houston 1963-2012: Obituary
> Whitney Houston: A life in pictures
> Whitney Houston: Greatest musical achievements - pictures
> Whitney Houston to dominate singles, album charts next week
> Bobby Brown: "I love you, Whitney"
Watch Whitney Houston and Kevin Costner in The Bodyguard below: