The fight was ultimately signed, but Joshua was clearly not impressed by the Kiwis' tactics.
"Do you know what it is with Parker and his team?" he continued. "Behind the scenes they're different, a lot of the things that they say are different.
"I've seen some of the emails that Parker's manager sent Eddie and they say some really backstabbing things, but in your face they shake your hand and that's not my type at all."
In particular, Joshua and his promoter Eddie Hearn took issue with Parker's jibes at his supposed "glass chin".
Hearn added: "In the build up to his fight they were goading Anthony Joshua: 'He's got a glass chin, he's got stamina issues, he's got no heart.'
"Then the fight gets signed and we give them the platform at the press conference to look him in the eye and tell him. He couldn't do it, he couldn't pull the trigger!
"We don't mind the hype, we like the criticism, but say it to us!"
Joshua held a media workout earlier today at his training base in Sheffield, where he promised fight fans that "there will be blood" when he fights Parker.
The 28-year-old also warned Parker that he is a "different animal".
"Every fight and training camp has been something to learn from," he told Sky Sports.
"Who I was for my last training camp, I just feel like I'm a different animal, more fine-tuned. I don't just work hard anymore, I work smart, I'm becoming a real student of the game.
But Joshua insists he isn't underestimating Parker, who Hearn has described as his toughest fight to date.
"Parker is a phenomenal champion - tough, he has his (Samoan) heritage and he wants to prove he's a worthy champion," Joshua said.
"Anyone I fight, they always come 30 per cent better than what I've seen so I can't expect the same old Parker in the ring on March 31. I've seen there's been a lot of talk about the future but my future ends on March 31 [April 1 NZ time].
"That's where my goal is and that's where I'm focused on.... I can't take my eye of this guy. He's talented and he wants to prove himself."
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