The npower League Two outfit overcame Barclays Premier League side Aston Villa 4-3 on aggregate despite losing the second leg 2-1 at Villa Park.
Parkinson said: "We said to the lads before that there was a chance to make history but, while we knew that, we had to focus on the key elements in the game to get us there.
"I felt we certainly did that in the second half. These lads will be remembered in the history of Bradford City for years to come.
"There's a 1911 lounge at the club to celebrate the cup victory of that year. Well, in years to come, there will be a lounge named after this cup run and these players because of what they've achieved."