The former Manchester United player,who has had management spells with Crystal Palace and Reading, quit after a 3-0 home league defeat to Millwall and a League Cup exit to Southend on Tuesday night.
"It's a shock and a shame because Steve is a very good manager and a great asset to football but I suppose he's reached that stage where he doesn't need to carry on working if he is not enjoying it," said Boothroyd to the CT.
Keith Millen has replaced Coppell at Ashton Gate and has been given a three year contract.