Manning was recruited after Norwich decided not to give the job to former England midfielder Jack Wilshere, who was in interim charge for the final two games of last season and is now manager at Luton Town.
Manning was born in Norwich and played in their academy before switching briefly to Ipswich and then dropping into non-league football.
He began his coaching career with Belgian club Lommel and had spells in charge at MK Dons and Oxford United before joining Bristol City in November 2023.
The Norwich squad was transformed by 12 signings during the summer transfer window, but the club sold Borja Sainz, who supplied 18 goals last season, to Porto for £14.25m, and Marcelino Nunez to rivals Ipswich for £10m.
United States international Josh Sargent scored six goals in five league and cup games at the start of the campaign but has none in the past 11 – and no-one else has managed more than Mathias Kvistgaarden and Jovon Makama’s three.
In his final post-match interview with BBC Radio Norfolk, Manning – who was recently given the public backing of majority shareholder Mark Attanasio – said: “I don’t live my life with regrets, it’s part of my journey.
“I’m learning, I’m hurting, I’m frustrated and I’m hugely disappointed, because this is a club I care deeply about.
“I didn’t come here to be where we are. But we are, so I will do a lot of learning as to why.”
His assistant Chris Hogg and analyst James Karuse have also left the club.