But the British star hit back at the claims by accusing his opponent's team of spreading "fake news".
The 28-year-old Joshua recalled the three times he had suffered knockdowns, telling the Parker camp: "A lot of people who have spoke about me getting dropped have used it as a publicity stunt, used it as a PR stunt.you are using it as well".
Scroll down to see AJ open up on the three times he has been genuinely hurt during a fight.
"The first was the European championships when only two weeks before I had been called back into the [Great Britain amateur] programme because I was banned from the GB team. I guess it was my team that got under his skin but I fronted that". "I got stopped. When your tank is empty, it's hard to perform".
'The second time was with David Price, I came out of a police cell the day before and went up there to spar. I don't want to come here and demonise Parker and say everything he has done is rubbish and anyone can walk into a gym and achieve what he has done because what he has done is phenomenal, it's history, it's groundbreaking. David Price is a puncher and that was down to a lack of experience.
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"The rumours that you have heard, they're all fake news". Hand on my heart.
WBO champion Parker is unbeaten in 24, with 18 knockouts, and he and his camp have brought attention to past occasions where Joshua was knocked down in the ring as amateur and professional. "Every time I am tested", Joshua said in his hometown of London.
Watch Iain Lee talk about what really went down on I'm A Celebrity, the ups and downs of his career, and his challenges with mental health only on Unfiltered with James O'Brien. He knows mine. I know his weaknesses. "I know his weaknesses and he thinks he knows my weaknesses", he told reporters.
Anthony Joshua says he's not taking anything for granted in his world title fight against Joseph Parker. "Can not wait to train, can not wait to be back, to put on a great performance, hopefully catch him on the chin and knock him out".
Joshua added: "It is an honour to be up here with another world champion".