"I would never want that tape shown," Stainton told talk-show host Larry King. "It should be destroyed."
Wednesday's memorial ceremony was broadcast live in the US on Animal Planet to an audience of 90 million, as well as across Australia and parts of Asia. Stainton now says the ceremony may be released on DVD.
"We have been discussing [a DVD release]," a Stainton spokesperson told The Sydney Morning Herald.
Irwin died on September 4 while swimming near The Great Barrier Reef when a giant bull stingray lashed out with its tail, piercing him in the heart.
Australian Prime Minister John Howard and Australian folk singer John Williamson joined thousands of Irwin fans in the Queensland zoo Crocoseum, while videotaped tributes were played from Russell Crowe, Kevin Costner, Cameron Diaz, and Justin Timberlake. The zoo staff spelled out Irwin's catchphrase "crikey" in yellow flowers.