The League Two club, who finished the game with 10 men, were ruthlessly dispatched by their Premier League opponents at Wembley Stadium on Sunday.
"I am disappointed obviously," Parkinson told BBC Sport. "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."
Bradford knocked out top-flight opposition in the form of Wigan Athletic, Arsenal and Aston Villa on their way to the final.