The Black Cats were beaten finalists in the competition last season, but were dumped out at the Stadium of Light as Marc Muniesa's brace fired the Potters into the fourth round, despite Jozy Altidore's 16th-minute opener.
"We are obviously disappointed with the result because the lads had a great cup run last year and we wanted to emulate that during this campaign," Jones told the club's official website.
"We conceded a couple of easy goals which could have been prevented and created a few chances that we should have taken. It is a recipe for losing the game and unfortunately that's what happened."
Sunderland face Swansea City in their next match in the Premier League on Saturday.