The Bantams were already trailing 3-0 in the Capital One Cup final when their goalkeeper was sent from the field after bringing down Jonathan de Guzman in the box
The Bantams were already trailing by three goals at Wembley when Duke was sent from the field for tripping Jonathan de Guzman in the box.
And Parkinson believes that a yellow card would have proved a sufficient punishment, given that Swansea was already in the ascendency.
"Conceding goals when we did did not help and we had our goalkeeper sent off," he told Radio 5 Live. "I felt the referee could have given him a yellow card.
"At 3-0 down I felt he could have used his common sense, but then they scored the fourth and that was it.
"Everyone watching the game would have felt that was harsh - there was no need to send him off. Were we going to come back and win 5-4? No."
The 45-year-old went on to admit that Bradford had been outclassed by Michael Laudrup's men during Sunday's showpiece.
He added:"I am disappointed obviously. We were not able to make a game of it but Swansea are an outstanding team.
"We found it tough but a lot of Premier League teams find it tough against Swansea."
With Bradford eight points short of a League Two playoff place, Parkinson underlined the importance of his side's focus now returning to their league commitments.
He said: "We will dust ourselves down. We have enjoyed the whole experience and we will go back up to Bradford and enjoy the last 15 league games. We have a chance of promotion so we will make a go of it."