The 36-year-old quit as McGregor's sparring partner last week, saying that he felt "exploited" by the Irishman's camp after several training pictures were released to the press, one showing Malignaggi on the canvas.
Malignaggi, who was also concerned about being asked to spar for 12 rounds, told MMA Hour: "The funny thing about the push down was this - it was during one of his worst moments. He pushed me down on the floor to try to catch a break and the instant I went down I got back up.
"I started to take it to him right after that. I told him, 'you get no breaks here', and I started to hit him with more body shots. I said, 'take those, they don't feel good' and I could hear him whimper off the body shots, too."
MMA fighter McGregor faces five-weight world champion Floyd Mayweather Jr in his boxing debut in Las Vegas on August 26.