The music mogul described the 25-year-old as a "sweet and funny girl", and said her passing was a "tragedy".
Speaking to Channel 5 news at the launch of Britain's Got Talent, Simon said, "Like I said on the night, I met her, she was a sweet and funny girl. It's a tragedy at that age.
Simon: "She was a sweet and funny girl"
"That whole family, what they’ve had to go through. I feel really bad for them."
He added, "What can you say in a situation like that? Other than everyone is obviously thinking about them, they need some privacy to get over it in their own time.
"If it happened to me, I don't know how I would deal with that."
Mystery still surrounds Peaches' death. A post-mortem proved to be inconclusive pending the results of toxicology tests, meaning her grieving family must continue to wait for answers.
Peaches with her two sons Astala and Phaedra
The mum-of-two was found at her home in Wroxham, Kent on Monday, and police have said her death is being treated as "non-suspicious" and "unexplained".
"Officers continue to investigate the circumstances surrounding the death in order to compile a reports for the coroner," a spokesperson said. "The result of a toxicology report can take several weeks."
On Wednesday, Peaches' father Bob Geldof flew back to the UK from America to reunite with his heartbroken family, including Peaches' husband Thomas Cohen and grandchildren Astala, 23 months, and Phaedra, almost one.
He issued an emotional statement following his daughter's death.
Bob Geldof flew back from the US after receiving the news of Peaches' death
"Peaches has died. We are beyond pain," he said. "She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us.
"Writing 'was' destroys me afresh. What a beautiful child. How is this possible that we will not see her again? How is that bearable?
"We loved her and will cherish her forever. How sad that sentence is.
"Tom and her sons Astala and Phaedra will always belong in our family, fractured so often, but never broken."
In his own statement, Peaches' husband added, "My beloved wife Peaches was adored by myself and her two sons Astala and Phaedra and I shall bring them up with their mother in their hearts every day. We shall love her forever."