Walter Isaacson, author of the 2011 "Steve Jobs" biography, on Monday revealed to a greater extent the pointed criticism that Jobs had about Tim Cook, whom he handpicked as Apple CEO before his death.

"I softened it in the book a bit. Sometimes I soften things that I thought were too harsh," Isaacson told CNBC. "In my book, Steve says how Tim Cook can do everything, and then he looked at me and said, 'Tim's not a product person.'"

On "Squawk Box," Isaacson said that Jobs in interviews for the book went further than that. "Sometimes Steve, when he was in pain and it was problematic and he, he was angry, he would say more things than [Cook] was not a product person. I felt I would put in the specific things that were relevant to the reader but not the complaints." Isaacson did not elaborate further about those complaints.

Isaacson's biography was published on Oct. 24, 2011 — 19 days after Steve Jobs died from pancreatic cancer at the age of 56.

The author's remarks on the Jobs-Cook dynamic came as Monday's Apple discussion on the show turned to the announcement last month that design chief Jony Ive was leaving the company. Jobs and Ive were really close.

"Every day when Jobs was in the office in Cupertino, he would go at midday to that sort of big locked door that went to the design studio; be brought in and everybody else would be ushered out. And he would talk table to table with Jony. They would feel not just the phone but the plug. The jack, the way the wire coiled. Jobs at his core was a product person," Isaacson said.

"What I think you are seeing now is a company that can execute pretty well. But it doesn't have at its core these two spiritual soulmates who just lived and breathed the beauty of products," Isaacson said. "I think it would have been better to have the design chiefs report directly to [Cook] ... for him to go to the design studio at least once a week."

Cook and Apple were not immediately available to respond to CNBC's request for comments on the Isaacson interview.

Shares of Apple were under pressure Monday after Rosenblatt Securities downgraded the stock to "sell" from "neutral," saying there's "less reward" for ownership. However, Rosenblatt maintained its 12-month, $150-per-share price target.

Apple shares, which have soared nearly 30% so far this year, closed slightly lower Friday to around $204 each.