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 were already in the ascendency.
|15/2||Bradford are 15/2 to be promoted from League Two with Bet365|
"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 play-off 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."