Katie Nicholl, who has previously written Kate: The Future Queen about the Duchess of Cambridge, told OK! Magazine that the mum-of-three had found the interview hard to digest.
A key moment in the programme came when interviewer Oprah Winfrey asked Meghan to clarify what happened at the bridesmaid dress fitting for her wedding.
The Duchess of Sussex claimed that, contrary to previous newspaper reports, Kate had made her cry rather than the other way around.
Nicholl said that people around the future queen noticed she was low while performing her royal duties last week.
"Behind closed doors, she has been saddened, disappointed and hurt," the royal writer said.
Nicholl said there were different versions of the bridesmaid story circulating, in addition to the one put forward by Meghan.
"Kate felt it was all sorted, so to have it brought up again was mortifying. Kate is not in a position to respond and Meghan and Harry know that," she continued.
"Kate has never wanted any suggestion of a rift with Meghan to come out in the press, so for this story to be circulating is very hard."
The dress fitting row has become the focus of much debate, with Meghan insisting she was the one left in tears by the incident when she spoke to Oprah Winfrey.
"A few days before the wedding, she was upset about something pertaining - yes, the issue was correct - about flower girl dresses, and it made me cry, and it really hurt my feelings," said Meghan.
Meghan, Kate, designer Clare Waight Keller, two assistants from the Givenchy fashion house and Melissa Toubati, Meghan's aide were at the fitting for Princess Charlotte.
But it's believed the dress didn't fit, and with little time left for changes to be made, stress began to mount and tears were shed, just weeks after Kate gave birth to Prince Louis.
But in contrast to previous claims, sources have now said it was both Meghan and Kate who were left in tears after the ordeal, reports the Sun on Sunday.
A source said: "Both women were clearly shaken by the bridesmaid’s fitting incident.
