Bradford were 3-0 down at the time and Parkinson said that a yellow card would have offered sufficient punishment.
"Conceding goals when we did, did not help and we had our keeper sent off. I felt the referee could have given a yellow card," Parkinson told BBC Radio 5 Live.
"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."
Parkinson went on to admit that although he was disappointed, his side were outclassed by Swansea.