Postgate's other TV work included Noggin The Nog, Ivor The Engine and The Clangers.
He died at a nursing home in Broadstairs, Kent on Monday.
His shows were created by his own company Smallfilms, which he developed with puppeteer Peter Firmin. The duo began the company in a disused cowshed in Kent.
Postgate famously narrated all his Smallfilms programmes
Bagpuss, which ran for 13 episodes from 1974, is regularly voted one of Britain's best-loved children's television shows, and earlier this year its rights were sold to media company Coolabi for £400,000.
Postgate stopped working in 1987, complaining that TV commissioners were not interested in his brand of children's entertainment anymore.