"You do not take somebody in that room that you believe is a danger to herself or a danger to Paula," Nigel Lythgoe told PEOPLE at Thursday's Superstars of Dance press day in Los Angeles. "That would not enter our heads.
On Nov. 11, police discovered Goodspeed dead of an apparent suicide outside of Abdul's Los Angeles home.
"The very fact that this happened, I'm really sad for her family," said Lythgoe. "It happened about four weeks ago. For it to come back four weeks later, I'm really sad we're still talking about it."
Abdul, 46, said earlier this week in an XM Satellite Radio interview that she had asked Idol producers not to put Goodspeed on the program. "I said, 'This girl is a stalker of mine. Please do not let her in.' Everyone knew. I was shaking," Abdul said.
Producer Called Goodspeed 'Lovely'But that is not the way Lythgoe, who left Idol over the summer, says he remembers it.
"[Goodspeed] had been through an audition process with the producers, an audition process with the executive producers, and we were wheeling her in as a huge fan of Paula Abdul," Lythgoe said. "This is what we knew: She was a great fan, she was a lovely girl. And a great fan of Paula."
Lythgoe said doesn't remember Abdul's request to have Goodspeed removed. "This is three years ago," he said. "I honestly say I can't remember the conversation. If Paula said, that's what she said, I believe her."
Lythgoe added: "We've seen over 700,000 contestants. And one has made a terrible, terrible mistake. If you're an odds man, they are great odds."
As for Abdul, Lythgoe said he harbors no ill will toward the Idol judge.
"I'm not angry with Paula," he said. "I think Paula's in a position of: 'It wasn't my fault,' and reaching out from that point of view. For her family's sake, it should really be dropped."
Lythgoe, who left American Idol as a producer over the summer, is now producing, So You Think You Can Dance and January's new series on NBC, Superstars of Dance.
2000: Brooke Shields' stalker arrested after a 15-year obsession
2005: Paula opens up about battling chronic pain