Jones, who died Feb. 29 at age 66, was "a very Christian hero" who conducted himself "with humility and caring for others," the Rev. Frank O'Loughlin said at the closed-door service at Holy Cross Catholic Church.
Although the funeral was held only for close family and friends, a copy of his sermon was provided to the Associated Press.
"He wrote about a quiet, gentle, contented people," O'Loughlin said. "A people for whom life was bright, neighbors friends, daydream believers with an absolute absence of burden who took themselves lightly – lighter than air. Wasn't that what David conveyed to the world, a blissful lightness of being?"
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Jones's three bandmates from the Monkees didn't attend; they said earlier they didn't want to bring unwanted attention.
But the Monkees' Peter Tork remembered the British-born Jones as the consummate professional with a wacky sense of humor and a keen sense of empathy.
"Davy could be incredibly insightful," Tork tells PEOPLE. "Some of my best heart-to-heart moments have been with him. And he was a tremendous presence and a world-class performer. It's very hard to believe he's gone."
For more on the beloved musician – and his life in pictures – pick up the latest issue of PEOPLE, on newsstands Friday