The midfielder, who netted in the successful shootout, insisted the Bantams were given a tougher examination in a recent league encounter with Torquay United, than in their clash with the Premier League side.
He told reporters: "I’d feel embarrassed without a shadow of a doubt. No disrespect to our lads, but they should be beating Bradford City.
"I think Torquay gave us a harder game. It was like a role reversal against them. Torquay really defended well against us and we defended really well against Arsenal.
"The lads were unbelievable. It was one of those nights when you just had to be here to witness it.
"To beat a full strength Arsenal in the Capital One Cup quarter-final is what dreams are made of and what you play football for.
"We have a massive team spirit and that’s what happened. It was one of those nights - cold, the pitch was frosty - and then it is about who wants to win the most, and I think we did.
"I think the team who wants to win most more often than not does so, and we were full value for it. The lads were unbelievable and, as I said, it’s just a dream come true."
Tuesday night's win was the Yorkshire club's ninth-successive shootout success and Jones believes the momentum swung in their favour when it had to be decided by spot-kicks, but believes his side were well worth the victory.
He added: "I think it was Arsene Wenger’s worst nightmare going to penalties. The lads were full of confidence, I think that showed and obviously now we’re in the semi-final.
"We were surprised how comfortable we were at times. They didn’t really have too many shots on goal. They tried to play too much football at times, especially down the middle."
Jones could not contain his surprise at the strength of the Gunners' line-up and admits Arsene Wenger and his side will regret a missed opportunity in this year's competition.
He revealed: "When we saw their team-sheet, we couldn’t believe it. [Assistant manager] Steve Parkin wrote their side down and at the bottom he wrote ‘poor team’ with an exclamation mark.
"I thought they would have a lot of youth players and a bit of experience, but nothing like that turned up.
"They came here and it was probably the best chance of a trophy they’ll have this year."