The League Two side are on the verge of claiming their third Premier League scalp in the competition having already disposed of Wigan and the Gunners.
Goals from Nahki Wells, Rory McArdle and Carl McHugh gave the underdogs a commanding advantage to take to Villa Park on 22 January, while Andreas Weimann's strike was the only setback on a memorable night for the Bantams at Valley Parade.
Asked if the result was more satisfying than their victory over Arsenal, Parkinson said: "Yes. To score three goals against a Premier League team is an outstanding achievement. We played so well.
"They came with a really attacking line-up but they left space and we passed the ball so well. They had chances but so did we.
"We don't want to get carried away with our celebrations because we still have to go to Villa Park for the second leg but the lads can enjoy themselves tonight.
"Now we can go there and really enjoy it because the pressure will be on Villa."
Nineteen-year-old defender McHugh was facing his footballing idol, Villa keeper Shay Given, and was delighted to have scored past him.
Like Given, McHugh hails from the Republic of Ireland and he said: "It's all a bit of a blur. It's unbelievable to score against him, with us coming from the same part of Ireland.
"I have watched him play in World Cups for Ireland and it's a dream come true. I was determined to make sure we got the two-goal lead. I didn't care how I got my head on it."
Of equal importance was McArdle's goal and he admitted to being in a state of shock at what had happened.
"It's not quite sunk in, it's similar to the Arsenal game, emotions are here, there and everywhere," he said.
"It's going to be a tough test ahead but we've more than done well enough to build a platform and if we can do that in the second leg, we won't be far away."