Coventry have parted company with manager Micky Adams following a board meeting at the Ricoh Arena.
The third-round loss extended the Sky Blues' winless streak to eight matches in all competitions.
The slump started with a 5-0 demolition by midlands rivals West Brom on December 16 and Coventry have taken just one point from six league games since, slipping to 16th in the Championship.
Saturday's dismal 4-2 league defeat to Crystal Palace increased the pressure on the under-fire boss, who had repeatedly insisted he would not resign.
Adams told Sky Sports: 'I am devastated. I am bitterly disappointed but I understand and respect the decision and I will move on.
'Unfortunately the football industry is such that you do not get time but I genuinely believe I could have turned it around.
'It's not been a disastrous tenure but as I said before I will move on and I want to get back into work as soon as possible.'
Adams refused to blame the club's indifferent season on the loss of star winger Gary McSheffrey, who joined rivals Birmingham for £4million in August.
'I am not here to throw stones at anyone,' he added.
'I have too much respect for the club but the sale was a big turning point for everyone. But I've been supported as well as I could have been by everyone here.
'All my best wishes go to the football club and to their future success, unfortunately I won't be part of it.
'The players have to pick themselves up on Monday at Plymouth and show everybody that they are good players.'
A statement, released by Coventry on behalf of managing director Paul Fletcher, said: 'This is a decision that the board of Coventry City Football Club has not taken lightly.
'Everyone at the club has supported Micky 100%, but unfortunately, results have not gone as well as we all anticipated given the substantial investment in the team.
'We are committed to our three-year quest to get Coventry City back into the Premiership and believe that tough decisions like this will sometimes be needed to fulfil that aim as is sadly the case today.
'I join the board in wishing Micky all the best for the future.'