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.
Former shelf-stacker James Hanson scored the decisive second-leg goal to set up a final meeting with Swansea or Chelsea. Christian Benteke and Andreas Weimann netted for Villa.
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."
Bradford have twice gone into administration since being relegated from the Premier League more than a decade ago.
Hanson is the only player at the club to have cost a transfer fee - £7,500 when he moved from Guiseley three seasons ago.
But Parkinson is confident the current cup run, in which Bradford have also knocked out Wigan and Arsenal, will help to make the Bantams financially secure for the foreseeable future.
He said: "Financially, the money we have earned up until this point has been fantastic. But to go to Wembley is going to keep the club going for quite a while, I imagine. For the city of Bradford, it's massive and I really feel that this can galvanise the area."
- Sports & Recreation