The Potters' shock defeat followed on from a poor run of form in the Premier League which has left the club in the relegation zone.
"I don't like Mark Hughes. I don't think he is a good manager," Barton told talkSPORT on Tuesday. "I've worked with him at QPR. He is a terrible manager. At QPR, he was awful.
"Hughes has made Stoke progressively worse. They got to a League Cup semi-final, which Bristol City have done from the Championship.
"I don't think he progressed Stoke. He increased the wage budget and he hasn't made them better."
Stoke finished ninth in the Premier League in each of Hughes's first three seasons in charge but ended the 2016-17 campaign in 13th place and have won only five of their 22 games this term.