The League Two club embarrassed their heavyweight Premier League visitors at Valley Parade with a 3-2 win on penalties after a 1-1 draw after extra time.
And midfielder Jones, whose free-kick set up Garry Thompson's opener which was eventually cancelled out by Thomas Vermaelen, was left in shock.
"This has got to be one of the best nights of my life," Jones told Sky Sports.
He added: "I cannot believe we have just knocked Arsenal out of the Capital One Cup.
"It was 11 v 11 and we had to keep our shape and frustrate them. I am lost for words."
Goalkeeper Matt Duke saved a penalty from Santi Cazorla in the shoot-out as Bradford recorded a record-breaking ninth successive win on penalties.
He said: "We set our stall out and the men in front of me were fantastic. We are really fit as a team and that showed."
Duke added regarding the penalties: "I was confident we would do it. We have got some great penalty-takers and I always fancied myself to save a couple."