The League Two outfit overcame 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 either 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."
He added: "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.
"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."
Victory against either Swansea City or Chelsea at Wembley on February 24 would earn Bradford a place in Europe for the first time since they appeared in the now defunct Intertoto Cup in 2000.
"If we get into Europe I'll have to start learning some languages!" Bradford chairman Mark Lawn said.
"I don't care who we get in the final, they will probably both batter us. Chelsea will have to declare at halftime if we play them!"
Villa, trailing 3-1 from the first leg, went ahead through Christian Benteke but James Hanson's 55th-minute header calmed Bradford's nerves and they held on despite Andreas Weimann's late effort for the five-times League Cup winners.
Hanson said he had never been to Wembley before.
"I can't believe it, it really hasn't sunk in yet," said the 25-year-old. "The lads dug in in the first half and I thought we were going to have our backs to the wall.
"But we were actually pretty comfortable in the second half and we held on well."
Keeper Matt Duke, a hero of penalty shootout wins against Premier League Wigan Athletic and, most notably, a strong Arsenal side in the last eight, summed up the mood.
"I'm speechless. The lads had a fantastic game tonight and the fans as well, it'll be a great day at Wembley for them," he said. "Everyone had a great game.
"As a kid playing football, you dream of Wembley and we're going to do it. We're going to take a League Two club to Wembley, we're going to take a massive following, it's going to be an amazing day and I'm looking forward to it."
Villa had looked set to spoil the party but paid the price for poor defending as the gloom deepened for the Midlands club.
"That is the worst day of the season. We had two chances to do it and haven't done it," Lambert said.
"We've lost four goals from set-pieces over two games which is not good enough. I am embarrassed. We will never have a better chance to reach the final."