The preacher's passionate 14-minute sermon was one of the stand-out moments of Saturday's ceremony.
Entitled The Power of Love, it was the most tweeted-about moment of the day, according to Twitter.
But Rev Curry said he thought the invitation to speak at Harry and Meghan's wedding was a prank.
He told ITV's Good Morning Britain: "I thought somebody was doing an April Fools' joke on me. I just didn't in my wildest imagination..."
The bishop said he "had no idea" his speech had caused such a stir, adding: "When I sat down from the sermon I remember thinking to myself, I hope that was OK."
Turning to the newlywed couple, Rev Curry added: "They're going to work to make this world better and empowering women is one of the ways we do that."
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