The Sun newspaper reports that Cohen was in a ‘zombie like state’ at the service in the historic church where the couple were married just two years ago.
A host of celebrities from the music and television worlds attended the private service for the 25-year-old at St Mary Magdalene and St Lawrence Church in Davington, Kent.
Kate Moss, Sarah Ferguson, Jo Wood, Jools Holland and Jaime Winstone were amongst those spotted as Bob Geldof wanted all her friends to attend so they could lend their support to Tom and his two sons with Peaches, Astala and Phaedra.
Still awaiting confirmation of what caused his daughter’s death, Geldof paid a moving tribute to her.
An insider told the Sun: “Bob was stoic and held it together. His voice only broke a couple of times.
“Thomas, however, is struggling to cope and was walking around in a daze, like a zombie. His family are very worried about him.
“Bob wanted all the celebrities and her friends to be there for her children. He has made it clear he doesn’t want the kids to be emotionally on their own, and for Tom to have as much help as he needs.
“He also made it clear this wasn’t about one day. Peaches would want them there for her children in the future.”
The Sun reports that Peaches’ body was taken into the church in a coffin with a picture of her, Tom, their sons and pets drawn on the side.
The 150 mourners attended a wake in Geldof’s nearby country mansion after the funeral.
The insider added: “The service was upbeat. It was highlighting the good moments. Bob made it clear it was to be a positive day about celebrating the best of her life.
“Kate Moss got particularly emotional and was crying on Jamie’s [Hince, her husband] shoulder, while Sarah Ferguson was trying to comfort everyone.”
The report adds that the star’s death is still unexplained, with a post-mortem proving inconclusive and toxicology tests due back in a few weeks.