The 35-year-old pulled off a string of saves as the League Two side recorded a famous victory at Valley Parade.
Villa still favourites - Parkinson
"It is unreal. I can't believe we beat them. We thought we could get something but a 3-1 lead is fantastic," he said.
Bradford are seeking to become the first team from the fourth tier of English football to reach the final of the League Cup since Rochdale in 1962.
The Bantams, who beat Premier League Wigan and Arsenal on their way to the semi-finals, took an early lead through striker Nahki Wells.
Second-half headers from centre-halves Rory McArdle and Carl McHugh, either side of Andreas Weimann's goal for the visitors, gave Bradford a two-goal cushion to take to Villa Park.
Manager Phil Parkinson said: "We're absolutely delighted with the way we played, obviously, because from the first minute to the last the lads were tremendous.
"But equally we know we're only halfway there, we've got a very difficult job in a fortnight's time."
Robbie SavageFormer League Cup winner and BBC Radio 5 live pundit
"Gary Jones led by example in the middle of the park and goalkeeper Matt Duke was magnificent. They have all been terrific to beat a Premier League side. It was an unbelievable tie - one of the best I have ever seen. I still make Villa slight favourites though because they have the quality and Bradford could be nervous. Can you say Villa have been embarrassed tonight? I'm not sure you can, given that Bradford have played so well, but it will be very difficult for Paul Lambert to raise his players for the second leg."
"Against Arsenal it was a great night for us but I think the all-round performance tonight was better," he said. "Villa played a very attacking team and we had to defend well, and equally they left a lot of space on the pitch for us to play.
"Our quality players had to stay composed on the ball and they certainly did that."
Duke says a bright start in the return game in a fortnight will be key to their chances of reaching the final.
"We need to get a good start down there and get their fans on their backs," he added.
"They'll have tremendous support and we have to do what we did here tonight, but better.
"The main thing is we can't go there and be complacent because if we are then we will be punished. We haven't achieved anything yet."
Lambert critical of Villa defending
On his own performance, the former Burton and Hull man added: "It was one of those nights where you fancy yourself to make some saves.
"I think it's up amongst my best games. I've played a lot of standards from Sunday league finals upwards and I'm just thankful that tonight was one of those nights where you are able to make saves.
"I have to give credit to the lads in front of me because they were brilliant too."
Watch highlights of both semi-final first legs on The League Cup Show on BBC One & the BBC Sport website from 23:05 GMT on Wednesday, 9 January
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