He said he was already "distressed" as it was the first anniversary of his mum Pat's death, and the radio's discussion of the report had made him feel even worse.
Related ArticlesChelsea and Liverpool serve up a tale of the unexpectedAndy Burnham heckled during Hillsborough memorialMissing chef: father describes familys living nightmareMothers Day: 50 Most Memorable Mums in the artsFrank Lampard: Im in the form of my life at ChelseaLampard spoke out after his former fiancee Elen, 34, said he was "heartless", a "b------" and had "no emotion" about their break-up.
She claimed she and their daughters Luna, two, and Isla, one, were living in a small flat while Lampard had stayed in their £8.5 million townhouse which he had turned into a "bachelor pad" and was "seeing other girls."
In his call to the radio show Lampard indicated Elen had decided to move out of their home and he was fighting to get access to their children.
He told LBC's James O'Brien: "Unfortunately it has had a large impact on my relationship at home and I find it insulting that I wouldn't fight it tooth and nail, that's what I have spent time doing.
"You don't know anything about me. I find it insulting that you are insinuating that I am weak and scum because I have not fought tooth and nail.
"The hardest part of this whole break-up for me is not waking up with my kids every day. So before you start insinuating and calling people weak and scum on a radio station, sitting on a high horse which you are, because I hope one day your wife or girlfriend doesn't come to you and say she doesn't want to be with you, and that means you won't see the kids a few days a week.
"It breaks my heart - do you think I'm happy? Stop insinuating things. You're saying 'any man that lets his kids live in inferior circumstances to him is weak and scum.' You're insinuating that about me.
"My sister has been listening for the last half hour and the conversation has been about me. I don't want you to apologise, what I want you to do in future is when it comes to personal issues, and you're degrading to them as a human being . I grade myself as a human being as how well I bring up my kids.
"I have woken up sometimes and seen a newspaper report of me coming out of a bar or club and they take pictures of two different women who I have never ever spoken to and say I spent all night sitting next to them.
"Then I have to wake up and listen to idiots like you, I have to put up with it and I've got to keep my mouth shut.
"As I said to you earlier, my sister has been listening to this and it's the anniversary of my mum's death, so do you think my sister needs to hear you saying things like that on a radio station.
"Sometimes you need to think about things before you speak about them. I'll speak to you man to man about that, forget the radio station, I'll speak to you man to man."