Kathy Griffin on Zendaya Controversy

In her first interview since the controversy erupted over a joke about Zendaya on E!'s Fashion Police, Kathy Griffin admits that she wouldn't have made the crack if it were written for her.

In an interview with the Chicago Sun-Times' Splash Magazine, Griffin said Giuliana Rancic – who said that Zendaya and her dreadlocks look like "she smells like patchouli oil or weed" – should rely on her "great insider gossip" rather than the humor of others.

"I wouldn't have said the joke in the first place. Some dude wrote it for her," said Griffin, 54.

She went on to offer this advice for her Fashion Police costar: "Don't have anyone write you jokes or even suggest jokes for you on Fashion Police. You have enough great insider gossip from actually being on the red carpet. That's what fans want to hear the next day. Just talk and be yourself."

Griffin said she couldn't explain why Kelly Osbourne left the show, though she did say that "sometimes she seemed very upset at the mere seven tapings of Fashion Police we did together."

"I can tell you this ... I adore [the Osbourne] family. I've spent the most time with Sharon. She is the real deal. Love her!"

She added, "Kelly came to my house a couple of times when Joan [Rivers] was in the hospital, and we were consoling each other. I can tell you there was genuine love there. Oh, and of course, Ozzy is amazing."

Griffin also offered some fascinating insight into how the E! show is produced. She said she poo-pooed an idea to run a segment called "Whore Score" – and not just because the cutesy rhyme was deemed fun.

"I think we can do better," Griffin said. "Look, God knows my ... how shall I say ... repertoire over all these years on TV and live touring has used some language I wouldn't use today, but people just aren't into that stuff anymore and I get it."

"Name-calling and alliteration with no comedic context is simply the lowest hanging fruit," she said. "If I'm making fun of Oprah, I don't just scream, 'She's fat. G'night everybody.' I do an impression of her hilarious voice, I quote episodes of 'Favorite Things,' I even tell a story of my personal experience about being on her show. I do not say she's a terrible talk show host or actress. I do not say she isn't beautiful. She behaves in a way that my audiences have found amusing for years."