The hospital has stressed that Mrs Saldanha did not face any disciplinary action and it "was working hard to support her".
But the tragic nurse's family said she would have been "devastated" at unwittingly assisting a colleague in breaching medical confidentiality over the condition of pregnant Kate Middleton and had died of "shame".
Mrs Saldanha's brother Naveen said that his devoutly Catholic sister was a "proper and righteous person".
"She would have felt much shame about the incident," he said.
Mrs Saldanha, whose husband Benedict Barboza is an NHS accountant, moved to the UK 10 years ago from Mangalore, India.
The nurse's 49-year-old husband said he was "devastated" by her death while her 14-year-daughter Lisha posted on Facebook: "I miss you. I love you."
They and her 16-year-old son Junal were said to be "shocked and inconsolable".
Speaking from India, where Jacintha was born, her mother-in-law Carmine Barboza said that in the days before the apparent suicide the extended family were not aware of the prank call.
Carmine (69) said: "Benedict calls every day but neither he nor Jacintha said anything about what had happened. Everything seemed normal.
"Then we got a call from Benedict informing us that Jacintha had died.
"He was crying and couldn't speak much.
"It is hard to believe that Jacintha could commit suicide. She wasn't the type of woman to do it."
Benedict is said to be seething with the DJs whose call duped his wife.