Having soaked up plenty of pressure from their Barclays Premier League hosts over the course of a contest that finished goalless after extra-time, the Bantams triumphed 4-2 on penalties - with Latics midfielders Shaun Maloney and Jordi Gomez both failing to convert their spot-kicks.
Asked how he felt about the victory, Parkinson said: "I am ecstatic. I thought it was a night of great discipline by the team. There were a lot of big hearts out there. Wigan give you problems that are ones we don't normally come up against in League Two, in terms of the movement of the team and their shape."
He added: "In the first 15 minutes we found it tough to cope with, but as the game went on, the discipline and commitment of the team grew. I am really proud of the team. Everyone stuck to the job over the 120 minutes and we got our rewards for that.
"If you play with commitment, desire and discipline like we did you do get rewarded and I am really pleased with the way we played."
Parkinson now has his sights set on drawing a big-name club in the last eight to provide Bradford with a cash boost that can aid their League Two promotion push. Parkinson, whose side are currently fifth in the fourth tier, said: "In terms of finance first of all, it is huge for the club, because there isn't a great deal of money at Bradford.
"But if we can get a good draw now, that is going to really help us for the rest of this season and going into next season. We have a lot of injuries at the moment, and if you look at how many players we had out, it will give you some understanding of what a great victory it was for us.
"But equally, there is going to be a time where I am going to want to knock on the chairman's door and say 'look, we are going to need to improve this squad' because teams at the top end of League Two as the season goes on do get better, and we are going to have to do that, especially with the injuries we have at the moment."
Wigan manager Roberto Martinez expressed his frustration at the Latics' inability to seal victory in a game he thought they had controlled well.
"I never felt that we lost concentration or allowed Bradford to have a big say in the game," said Martinez, who made nine changes to his first XI from Saturday's league win over West Ham. "I think we controlled it really well, and we were very unfortunate not to convert any of the chances. That was why it was a feeling of frustration more than anything."
Source: PA
Source: PA