"Further proof of that is that Dillian Whyte will simply not respond or talk about it," Higgins told the Herald of the headbutt. "He knows he benefitted from luck and won the fight because the referee made a mistake. I think he knows if he fought Joseph again on fair terms and with a proper camp he would lose the fight.
"As for Chisora and David Haye, we were promised formalisation of this fight for five or six weeks. About four or five deadlines have been missed. They know Joseph is at home in South Auckland with two kids with no trainer here. They know he has to travel to Las Vegas for a camp and then the UK. They were trying to run down the clock.
"The fight has fallen over because Eddie Hearn, David Haye and Dereck Chisora didn't come to terms.
"It's not trivial, it's an unfair playing field. We warned them weeks ago that we'd pull the pin if Joe wasn't given a proper camp and I don't think they believed us. I think they were laughing. When we pulled the pin they seemed shocked and suddenly were communicating again."
Speaking to the Herald after confirming that Parker would be happy to fight Tyson Fury should the terms be right, Higgins said either Whyte or Chisora should travel to New Zealand to fight Parker in a fight which would be popular in the UK and south Pacific in particular.
"They won't, they like their home advantage and referee and judging controversies," Higgins said. "They like the idea of Joe being jetlagged. If they were honorable they should come here. They will complain there's no money here but I call rubbish on that.
"We're calling them out. Give us an offer in the UK that's fair and we'll fight Whyte or Chisora. Alternatively, come to New Zealand and we'll put the fight on."
Higgins, meanwhile, confirmed Parker would be happy to fight Tyson Fury next.
"Some would say that would be the wrong fight for Joe next as Fury is a very tricky opponent. We kind of agree. Joe and I regard Tyson Fury as probably the best heavyweight in the world and the man to beat.
"We think he's better than Anthony Joshua and Deontay Wilder. That being said, boxing is a risk and return business. Joe has two young children under the age of two… he has to set up everyone [financially]. Fury v Parker would be a massive global event."