Briton Joshua, 27, knocked out Klitschko at Wembley Stadium in April and had hoped they would fight again in Las Vegas on November 11.
However, the Ukrainian, 41, announced his retirement earlier this month.
“In my heart of hearts I kind of knew he probably wouldn’t fight again,” said Joshua.
Klitschko’s nine-year reign as lineal world heavyweight champion was ended by Britain’s Tyson Fury in 2015 before he failed to regain the IBF and WBA titles in the 11th round defeat by Joshua.
“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.”
When asked how much of a disappointment Klitschko’s retirement was, Joshua replied, “Massive. It was probably even a disappointment for his management, his trainer (Johnathon Banks).”
Joshua has yet to finalise a date and venue for a fight with mandatory challenger Kubrat Pulev, who the Briton must face before December 2 or risk being stripped of his IBF belt.
The WBA have also ordered Joshua to defend his title against Cuba’s Luis Ortiz, having given them 30 days from August 3 to agree the fight.
Joshua added he respected Klitschko’s decision but contrasted it with 40-year-old Floyd Mayweather Jr, who is coming out of retirement to fight UFC lightweight champion Conor McGregor in Las Vegas on 26 August.
“Mayweather’s still going strong – Klitschko still had a good fight in him (in April’s defeat),” he said.
“I’m sure he’s still got a couple of other good fights in him.”
However, Joshua admitted even though “all looks good on the outside” Klitschko had “put his body through so many years impact”.
He added, “I’d appreciate it if we just sat down as gentlemen, and he gave me some experience he’s learned from over the years.”