Few gave the League One side much hope of avoiding defeat at Stamford Bridge on Saturday and a routine home win looked on the cards when Chelsea took a 2-0 lead.
However, goals from Jonathan Stead, Filipe Morais, Andy Halliday and Mark Yeates saw Bradford mount an incredible comeback to send the visiting fans wild as they celebrated one of the greatest FA Cup shocks in the competition's long history.
"In the first 20 minutes we did OK but then we conceded the first goal and gifted them a second," City boss Parkinson told BBC Sport.
"The goal we got back before half-time gave us belief and in the second half we really took the game to them.
"We are at our best when we do that, and the way the lads stuck to the job on the pitch was absolutely superb. Kicking to our supporters in the second half was a big factor too, they made it like a home game for us.
"It was almost surreal when the fourth goal went in. It took a while for what we have achieved to sink in.
"I thought we defended terrifically. We were up against world-class players but we stood up to the task. We looked like we could create all afternoon, and when you feel that way on the touchline you know you always have a chance.
"The day we got to the [2013] League Cup final, that result at Villa Park, was a very special one. But [beating Chelsea] in terms of the performance, that has to be the best.
"To come to the Premier League leaders and score four goals will take some beating. Hopefully we can beat it one day but it's terrific.
"After the game [Chelsea boss] Jose Mourinho came into the dressing room and shook the hands of all the players and staff, he was very complimentary about the way we approached the game.
"When we get back I am sure we will have a celebratory drink or two. I just want it to sink in slowly, to enjoy the moment."
