Joshua told the BBC the 25-year-old was "trying to mislead the public's opinion".
"I think it's not nice, I don't really respect it and I have no time for it," said the IBF and WBA champion, 28.
"What's he trying? Be the big bully? Demonise everything I have done?"
Speaking to BBC Sport he added: "In Formula 1, golf, tennis, rugby, they are very classy people, respectable about their peers.
"Then you have people like Joseph Parker holding a press conference talking about everything he thinks I am."
Should the fight happen, the winner could then face WBC title holder Deontay Wilder in a bout which could unify all four major titles in the heavyweight division.
Joshua beat Wladimir Klitschko to claim the WBA title in April, and followed that success with victory over Carlos Takam in October.
"This is the first time in my career where the talk has been about money," added Joshua. "That's what's holding it up.
"With Klitschko it wasn't about the money, it was about getting the fight together for the belts. With Parker it's a different story, and Wilder.
"No disrespect for them, they have their reasons, but I feel like the fans are not getting what they want.
"It would have been great to have it pencilled in now but it will happen in the future once they come to their senses.
"What they are offering is nothing, and what we are offering is 10 times better than what they can bring up themselves."
Duco boss David Higgins responded to Joshua's comments saying Parker is winning the psychological battle.
"Joseph Parker has already won the first round against Anthony Joshua. In the psychological battle, Joshua is rattled. He claims he is being demonised when Joseph has just given statements of fact," Higgins said.
"Remember Joshua called out Parker saying he wanted to unify. Parker has responded saying he will unify but has questioned what is a fair price for an unbeaten champion and who has the better chin?
"The fact Team Parker dared raise these questions has got under Joshua's skin. We are straight forward and open while the Joshua camp remains greedy and secretive."