The Potters were humiliated by League Two opposition in the third round, piling further pressure on a manager already on the brink of the sack.
And the weekend's 2-1 reverse proved to be the final straw, as hours after kick-off Stock confirmed he would not remain in the post.
"Stoke City can confirm that the contract of manager Mark Hughes has been terminated with immediate effect," the club stated in a string of comments posted on Twitter.
"We would like to thank Mark for all he has achieved for the Club over the last four and a half years, notably in guiding us to three successive ninth places finishes in the Premier League, and we wish him every success for the future.
"The Club will look to appoint a new manager as soon as possible and will be making no further comment at this time."
But after three impressive top-half finishes, the cracks began to appear last season when the Potters slumped to 13th.
The club currently languish in 18th in the Premier League, having won just five of their opening 22 matches.