The Bantams took a 3-1 lead into the second leg of their semi-final at Villa Park, but Christian Benteke reduced Villa's deficit in the 24th minute.
Villa dominated the first half but James Hanson equalised on 55 minutes and Bradford held on in a tense finish after Andreas Weimann's 89th-minute strike.
"Coming here two goals up we had a great chance," Parkinson said. "In the first half Villa were excellent but in the second I thought we played really well and thoroughly deserved it on the night.
"It's dreamland. We said we had a chance to make history and tonight we have done it. The lads were absolutely magnificent and what it means to the club and the city; it's absolutely tremendous.
"The supporters have come out in their numbers tonight and when we go to Wembley I think we can fill out our end.
"We just felt the first half we didn't pass the ball and in the second half we got hold of the ball and we had a period of possession.
"We said before the game that Villa are a very attack-minded team but they always leave us space on the pitch to exploit and I think at times we did that."
Despite knocking out Wigan, Arsenal and now Villa, Parkinson was cautious when asked about the chances of his side lifting the trophy against Swansea or Chelsea at Wembley on 24 February.
"I think that's going a bit far, but to get to Wembley is great for us," he added.
The Bantams boss also hopes the club will honour the players who have steered the side to Wembley.
"These lads will be remembered in the history of Bradford City for years to come," he said.
"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.
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 forseeable 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.
"Our supporters have stuck with the club through some really tough times. Over the last 10 years there hasn't been a great deal to cheer about being a Bradford City supporter.
"I'm so pleased that we've given them something so they can go into work and hold their heads up high and be proud of the club."
Parkinson admitted: "This has been the highlight of my career. It's got to be, to take the club to a Wembley final.
"A lot of players, a lot of managers, never get this opportunity to be in a semi-final. To take a team from League Two to Wembley is a dream and we are going to savour every minute."