The 43-year-old mother of two, who was best known from her time as a reporter with UTV, died in hospital last week, hours after revealing on social media that she was receiving palliative care for an illness.
Ms Kennedy, from Belfast, was the last surviving sibling of four children.
She, her sister Fiona and brothers Rory and Dara have all now died before their parents, Maura and Noel.
Retired cleric Father Sean McCartney, who also presided at the funerals of Fiona and Dara, told the congregation at the Good Shepherd Church in Belfast that he was not aware of another couple who had suffered so much loss.
“I’ve officiated at three of Maura and Noel’s children, of Dara and Fiona and now Aideen – it’s very difficult for me but so much more difficult for Maura and Noel,” he said.
“And I’m just delighted to be of some comfort and some support to them at this very difficult time.
“I know of no other couple who have suffered the loss of all of their children at any particular time.”
Fr McCartney spoke of the outpouring of “warm tributes” to Ms Kennedy since her death, which characterised her as someone who “lit up every room she went into”.
He said he was particularly impressed by the words of her long-time friend, DUP MLA Emma Little Pengelly, who described her as “beautiful, funny and kind”.
Former UTV colleagues were among those who joined Ms Kennedy’s friends and family at Tuesday morning’s funeral to say a final farewell.
A photo of the journalist with her children, Jacob and Eva, was placed at the front of the church, close to her wicker coffin.
During his homily, Fr McCartney referred to an interview Ms Kennedy gave to a Belfast newspaper several years ago.
In the article she described herself as someone who loved friends and family, who hated inequality and prejudice, and whose main regret in life was being unable to go back in time to say sorry to anyone she had hurt.
“What an inspiration,” said the cleric.
He added: “Her answer to those three questions just sums up the sort of person she was.
“When Noel rang me on Friday to say that Aideen had died, to say the least I was shocked, I was without words.
“I couldn’t believe that Maura and Noel… that they would suffer the death of their fourth (child), all their children.
“Noel said to me ‘It’s God’s will’.
“Well, I’m not happy about that phrase ‘It’s God’s will’. It’s used very often, but I struggle to know how it’s God’s will, how a mother of two young children in her early 40s… that that’s God’s will that she should be taken from us at this particular time.
“But it just shows you there are some questions that there are not really satisfactory answers to on this side of the grave.
“I certainly struggle. I always struggle with the death of a young mother particularly, (but also) any parent.”
Writing on Twitter on Friday about receiving palliative care, Ms Kennedy asked her followers to “keep an eye out” for her children, whom she described as the “kindest, sweetest most thoughtful kiddies”.
The reporter’s older sister, Fiona, died from cancer in 2016 at the age of 44, less than a year after their brother Dara died from a brain tumour aged 35.
Their older brother Rory was killed in a road accident when he was just a year old.
At the weekend, Ms Kennedy’s former employer said the UTV family was “deeply saddened” at the death of their friend.
“A truly gifted reporter, she spent many years at UTV bringing viewers stories from all over Northern Ireland,” the broadcaster said in a statement.