The 48-year-old has been a team captain on the show since it started 14 years ago, but said he was unhappy when Amstell replaced original host Mark Lamarr.
In a new book, Jupitus writes: ‘It struck me with Simon that people were being booked especially to have the piss taken out of them in a very overt fashion.
‘Mark didn't book people to rag on them, it was just in the flow of the show that people suddenly went a bit weird and Mark could turn on them.
‘It became something else with Simon and started to get a bit wearing.’
However, Amstell left the show last year and Jupitus will be back for the new series next month, when it returns with a series of guest hosts.
Jupitus’s new book –Good Morning Nantwich: Adventures in Breakfast Radio – is largely about his time with BBC6 Music, which he quit following a bust-up with controller Lesley Douglas over the playlist.
He says that quitting stand-up to do the breakfast show was 'the biggest mistake of the whole endeavour'.
He added: 'I could do gigs and tour really easily but I'd need six months of doing clubs to build the act up again. Standup is a young man's game. There are some remarkable acts out there, people are doing the O2 Arena. It has moved on. I haven't.'
The book has just been published by HarperCollins. Click here to order it.