The Bantams of League Two took a 3-1 lead to Villa Park this evening and only lost 2-1 to the Premier League side to set up a Wembley meeting with either Swansea City or Chelsea.
"I thought we had a great chance with the two goals from the first leg," Parkinson told Sky Sports News afterwards.
"First half Aston Villa were excellent but in the second half we played really well. It is dreamland. The lads were absolutely fantastic and what it means for the club and the city is absolutely tremendous.
"I think we could fill Wembley on our own. To win it might be going too far but to get to Wembley is great for us."
Bradford will find out their opponents when Swansea welcome Chelsea to the Liberty Stadium tomorrow having earned a two-goal lead from the first leg at Stamford Bridge.
The final will be played on Sunday, February 24.