The now-amended opinion piece initially read: “Mr Cameron has known pain and failure in his life, but it has always been limited failure and privileged pain.
“Even his experience of the NHS, which looked after his severely disabled son, has been that of the better-functioning and better-funded parts of the system.”
Speaking to Nick Ferrari in an interview broadcast on Thursday, Mr Cameron said: “There is no privilege in holding your eldest born child in your arms as their life drains away.
“From the little I saw of [the editorial] I couldn’t understand what they were trying to say, but fortunately it’s been deleted and apologised for so I think we can leave it there.”
Mr Cameron also said that he had recently deleted the Twitter app from his phone so “as a result, this whole argument about the Guardian editorial passed me by”.
He added: “It had been published, complained about, withdrawn and I got an apology from Katharine Viner, the editor of the Guardian, before I’d hardly even seen it.”
The former prime minister also extended an olive branch to Michael Gove in the interview, saying that “a lot of water has flown under the bridge” since the pair were driven apart by Brexit.
Mr Cameron told LBC he was moved by an “emotional and well-written” article by Mr Gove’s wife, Daily Mail columnist Sarah Vine, where she described the breakdown of their 20-year friendship.
He said that he “wants to try” to bury the hatchet with Mr Gove.
“It was just very difficult at the time of the referendum,” he added.
“I think the difficulty has just been that Michael was a very close member of the team and so watching what happened next was very painful and I did in some way think he had become a bit of a different person in all of it.”
Meanwhile, Mr Cameron told the BBC that he believes Boris Johnson put his own political career before the national interest when he chose to back Brexit.
Interviewed for the Cameron Years, Mr Cameron said: "By fighting for leave he was taking the romantic, nationalist, Conservative course, he'd look like a hero, and I don't think he expected for one minute they were going to win."
He added: "In the end I think, ultimately, he put what was good for his political career ahead of what he actually thought was good for the country."