Joshua was favourite to defeat the Ukrainian fighter and set up a showdown with Fury- providing the latter sees off Deontay Wilder in their trilogy fight which takes place next month.
But after Usyk won on points, taking Joshua's WBA, WBO and IBF titles in the process, Fury's not happy.
He said: "I was hoping Joshua could win the fight, but he couldn't - and that's none of my business.
"Did I watch the fight? Yes I did.
"Was I absolutely wounded that he won?
"Yes I was."
Fury will face Wilder on 9 October in Las Vegas in what will be their third fight.
Their first fight in December 2018 ended up as a draw but a dominant Fury won the next by a seventh round knockout in February 2020.
But Fury insists the only thing he cares about is beating Wilder.
He added: "The only thing I'm bothered about is beating Deontay Wilder, and that's the most dangerous heavyweight out there.
"In my opinion, Wilder beats Joshua, Usyk, all the rest of the division, comfortable - but he cannot beat me."
But Fury has no interest in gloating about Joshua's defeat and has urged the Watford-born fighter to "do what he has got to do".
He added: "I like to pick on someone who is doing well, successful, on top of the game - I don't like picking on people who are down and probably at their lowest point and probably mentally unstable and unwell with a big loss after such a long reign.
"Usyk did his job, he had to do what he had to do, and that's that, and Joshua has got to do what he has got to do."