IBF, WBA and IBO heavyweight champion Joshua knocked out veteran Klitschko in the 11th round in an epic Wembley bout in April.
It had been expected that Klitschko, whose nine-year reign as lineal world heavyweight champion was ended by Tyson Fury in 2015, would agree to a rematch with Joshua in Las Vegas.
However, the 41-year-old instead decided to hang up his gloves, a decision the unbeaten Joshua said he saw coming.
"In my heart of hearts I kind of knew he probably wouldn't fight again," he said.
"He was saying how obsessed he was with becoming heavyweight champion of the world again.
"If you fail at the first hurdle, you go again - [he] knew from my side I was ready for a rematch, making it clear that if he wants to go again, we'll go again.
"With Klitschko, we weren't hearing too much, so I just thought he was 50-50, but I had a feeling he might not fight again."
Asked how much of a disappointment Klitschko's decision was, he added: "Massive. It was probably even a disappointment for his management, his trainer [Johnathon Banks]."
Joshua, who is now set to face the mandatory challenger to his IBF belt Kubrat Pulev, hopes to receive advice from Klitschko.
"Take the financial side away, this is a sport when you get damaged mentally and internally," he added.
"It all looks good on the outside, but he's put his body through so many years of impact.
"He's quite intelligent so has other things to keep him busy, other interests outside of boxing, so he can make that decision comfortably with retiring and focusing his energy on other things.
"I know he's got some awards nights. I'd love to work with him, present him an award, and keep a good relationship now the fight's out the way.
"I'd appreciate it if we just sat down as gentlemen, and he gave me some experience he's learnt from over the years."
Photo by Getty Images. Caption: Anthony Joshua with Wladimir Klitschko