The 6ft 4in goalkeeper was sent off by referee Kevin Friend in the 56th minute after he brought down Swansea midfielder Jonathan De Guzman in the penalty area.
Duke, 35, who had no complaints with the penalty, felt Leicestershire official Friend could have shown some leniency instead of issuing a straight red card.
But after two goals apiece from Nathan Dyer and De Guzman and a first-half effort from Spanish striker Michu had reflected the gulf in class between the two sides, Duke vowed to return to the home of English football with the Bantams in the end-of-season play-offs.
"Today's a massive disappointment," said Duke.
"But when we come to reflect on this in a couple of days or at the end of the season, or even in a couple of year's time we'll appreciate what a fantastic achievement it was.
"Hopefully the fans have had a great day and no matter about the result that they've enjoyed it.
"Fingers crossed we'll be coming back in May to give them another great day.
"If we have a good run between now and the end of the season there's no reason why we can't get back in the play-offs."