James Hanson's goal proved enough to take the Bantams to Wembley, despite efforts from Christian Benteke and Andreas Weimann, after the League Two side had won the first leg 3-1 at home.
Phil Parkinson's side are the first club from the fourth tier to reach a cup final since Rochdale in 1962 and the players were ecstatic with their phenomenal achievement.
Jones told Sky Sports: "I'm lost for words. Just look at [the fans], that says everything. A fourth division club to get to Wembley is an absolutely magical thing. That's what happens in cups, magic does happen."
Goalscorer Hanson, a former supermarket shelf stacker, who had a pain-killing injection in his toe before the game, is now relishing a first trip to Wembley.
He added: "The lads dug in first half I thought it was going to be backs against the wall pretty much all night. It looked a bit nervy but I thought we were quite comfortable second half.
"I've never been [to Wembley]. It's been an amazing three years for me so I've just got to keep working hard and hopefully we'll get a trophy there."
Goalkeeper Matt Duke has played a key role in the Bantams cup run, with crucial saves in penalty shootouts against Premier League opposition Wigan and Arsenal.
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When asked if he believes in fairy tales, the former Hull City man responded: "I do now. I'm just speechless.
"The lads were fantastic again tonight. Look at the fans; it's going to be a great day at Wembley for us.
"Tonight was our final so we're just going to go [to Wembley] and have a great day.
"It's a dream. As a kid you dream of playing at Wembley and we're going to do it. We'll take a League Two club to Wembley with a massive following and it's just going to be an amazing day. I'm so looking forward to it.
"Whether we play Swansea or Chelsea, it's going to be a different game. If we do what we've done, we've got a chance."