Kevin Costner at Whitney Houston's Funeral: I Was 'Lucky' to Work with Her

Kevin Costner Speaks at Whitney Houston's Funeral
Whitney Houston and Kevin Costner
PictureGroup; StarTraks

02/18/2012 AT 02:40 PM EST

It was one of the most memorable love stories of the '90s: A former Secret Service agent, enlisted to look after a pop star thrust into danger in the spotlight, falls for the woman he's hired to protect.

But before The Bodyguard arrived in theaters in 1992, before the on-screen romance between Whitney Houston and Kevin Costner went down in cinema history, there was a simple question: Will it work?

Costner remembered that question at the late singer's funeral Saturday at the New Hope Baptist Church in Newark, N.J. There was a time, after all, that Houston doubted herself, he recalled to mourners gathered at the church and fans watching via Livestream.

"The greatest pop star in the world didn't think she was good enough," the actor, 57, said of Houston, who died last week at 48. "There were a thousand things that seemed to her to be wrong."

When she was screen-testing for the role, which was put in production a year later than slated because she was on tour, she asked herself, "Am I good enough? Am I pretty enough? Will they like me?"

As those attending the funeral laughed, Costner remembered how she almost sabotaged herself that day while re-touching her makeup with her own cosmetic products, which melted under the studio lighting.

"I wanted to tell her that the game was rigged, that I didn't care how the test went, that she could fall down and start speaking tongues," he said. "That I'd find a way to explain it as an extraordinary acting choice."

He added: "And gee, weren't we lucky to have her?"

PEOPLE is live streaming Houston's funeral online Saturday.

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