The Bodyguard actor delivered a moving speech at the New Jersey service in February, following Houston's death earlier that month.
In an interview with The Huffington Post, Costner confessed that he was unsure whether or not he wanted to react publicly to the loss of Houston, who he considered to be a close friend.
"I had consistently turned down doing sound bytes and going on news programmes to talk about Whitney. And the pressure began to build on some level about, 'Well, when are you going to say something, are you going to say something?'" Costner recalled.
"And the truth is, I don't really know how I feel at that moment about anything. Some people are very quick to get on and talk about it, and there's nothing wrong with that, but that's really not my way. And I actually didn't realise that it seemed that a lot of people did want to hear from me on some level. Sometimes you don't understand, and somebody has to say, 'People really do want to hear it'."
Costner continued: "And I was thinking, 'Oh my goodness', and I still didn't think any of the forums that I was seeing [like talkshows] were right, to be honest. There was one notion that maybe I would go on the Image Awards and present a film clip, which would be one or two lines and here's the clip, and she meant a lot more to me than that.
"When I got a call from Dionne Warwick, that's when I said I would come. And I'm not saying that was the right forum. It was the one where I chose to support Dionne Warwick at that moment."
Costner has previously said that he should have saved Houston, describing her as his "one true love".
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