He said: "I think it'd take some doing for anyone to do this again.
Mark LawrensonFootball Analyst
"Bradford dared to dream. They were helped by Villa who were very naive in the second half but don't take anything away from Bradford City. They played very good football and have been brilliant at set-pieces. My words aren't good enough for them."
"We had a really tough run. It wasn't just the Premier League teams, we had tough games with Notts County and Watford too."
Bradford went into the second-leg at Villa Park 3-1 up but Christian Benteke reduced the deficit for Villa.
James Hanson headed Bradford level on the night before Andreas Weimann scored a late goal for Villa.
Parkinson's side started their run to the final with an away tie at Notts County the week before the league campaign started in August.
En route to the final, the League Two side have seen off the Magpies, Watford, Burton and Premier League sides
and now Villa.
Their date at Wembley is the first time they have reached the final of a major competition since winning the FA Cup in 1911 and the first time a side from the fourth division has made the final since Rochdale in 1962.
Parkinson believes the money earned by the run to the final will secure the future of the club - as well as the place of his side in the history books.
Parkinson added: "These lads will be remembered in the history of Bradford City for years to come.
Phil McNultyChief football writer, BBC Sport
"Bradford fans will place their feat in the context of beating three teams from the top flight in succession, one 62 places above them in the league ladder over two legs, to reach Wembley, where their greatest moment may yet await them. It is, without doubt, one of the great cup achievements."
"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.
"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."
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