"I am a big fan of the show. I am blessed to be on the show. It's the greatest show on television all around the world and ... a gazillion people would love to be in my shoes," Abdul said at a meeting Tuesday of the Television Critics Association.
Abdul told Walters that Goodspeed was brought on the hit program "for entertainment value."
Goodspeed, who appeared on "Idol" several seasons ago, was found dead of an apparent suicide in a car near Abdul's Los Angeles home last November.
Pressed about it Tuesday, Abdul denied saying "anything disparaging about `American Idol' at all" or complaining to producers about Goodspeed.
When a reporter pointed out that Abdul was quoted as saying she had warned producers about the woman, Abdul replied: "Well, that is true. But that's that. I can't talk about it anymore. It's an ongoing police investigation."
Series executive producer Cecile Frot-Coutaz said what happened is "really, really sad" but should be put to rest.
"The truth is, we did know she (Goodspeed) was an extreme fan of Paula's. But from being a big fan to what happened, there's a big difference. And nobody could have known that it would actually happen."
Earlier Tuesday, Fox entertainment president Kevin Reilly was asked about Abdul's future with the show after her contract ends this year.
"Paula's an integral part of the show. As far as we're concerned, we want to have her as long as the show goes. When we get into those discussions, we'll see where Paula's head is at," Reilly said.