Malignaggi insists he dealt with McGregor handily in the latest bout of sparring on Tuesday but the Brooklyn boxer left McGregor's camp that same day after becoming unhappy with how the training was being portrayed on the Irishman's social media.
McGregor, famed for his UFC career, faces Floyd Mayweather in a boxing fight on August 26 in Las Vegas.
The 36-year-old says he will not be releasing any information about McGregor's game plan or what he's working on.
"I didn't want to become the story, and that's what this has turned into", he told ESPN on Thursday. But this has become a fiasco.
He added: "When I look back at the experience as a whole, not just sparring but as a whole, yes there was definitely an agenda beyond shadow of a doubt". "I understand it can't come out now, but Conor, if you have any balls, release what really happened".
Another shot by McGregor photographer Dave Fogarty shows Malignaggi falling backward on the canvas as McGregor stands over him. In a series of tweets on Saturday night, Malignaggi continued to criticize McGregor's ethics. I believe Conor and I have a mutual respect inside the ring, earned from each other with some good work over two sparring sessions.
Malignaggi wished McGregor well for the rest of the camp, but vowed to air his full version of events when the time is right.
"I wouldn't say that, a guy who's been retired 4 months n jus got back in gym 2 spar with him was kickin his ass by second sparring sesh lol".
Paddy Power would make a record loss if McGregor wins his upcoming fight against Floyd Mayweather.
McGregor, 29, is a two-weight UFC champion and the current lightweight titleholder.