The documentary, which aired just over a week ago, included a one-on-one interview with Markle, where she said she was "not OK". The confession came amid continued scrutiny from the British tabloid press, which has hounded the Duchess over her relationship with her father, and speculation over rifts within palace walls.
Prince Harry also substantiated long-running rumours of tensions between him and his brother, Prince William, heir to the British throne.
But speaking on 2GB this morning, Jones lashed the couple, calling their behaviour and comments in the documentary tone-deaf.
"In the documentary, we're told Meghan gives a rare glimpse of her new life and struggles as a royal and new mother," he said this morning.
"It borders on the insulting. Imagine spending time in Africa where you're around the poorest of the poor - people who have no possessions - and you're carrying on about how tough life is.
"Have these two people got no awareness at all?
"Has she ever wondered whether the poor people in Africa are OK? I've seen them, these poor kids with flies on their face and emaciated, with nothing, and the 38-year-old is complaining that people haven't asked if she was OK.
"She said she's struggling with duties — what duties? She's having six weeks off before Christmas for a holiday to LA!"
Jones also criticised the couple for their work regarding climate change, saying the pair took "private jets everywhere".
The couple came under fire earlier this year for sharing a quote urging others to "do your little bit of good," after it was revealed they regularly used private jets to travel the world.
Jones's comments come after a difficult year for the royal couple, who recently announced a series of lawsuits directed at the media.
