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Stead scored for the fifth successive round to help the League One side claim a quarter-final place.
The former Black Cats striker said expectations had increased following the 4-2 fourth-round win at Stamford Bridge last month.
He said: "This tops the Chelsea win because of the expectation on us."
Stead added to a first-half own goal from John O'Shea to seal Bradford's place in the last eight for the first time in 39 years.
The on-loan Huddersfield forward added:  "It's ended up, dare I say, a comfortable victory. The fans were magnificent and we made things hard for Sunderland right from the off, getting in their faces."
Stead scored just twice during a disappointing 18-month spell at the Stadium of Light, from June 2005 to January 2007.
The 31-year-old said that did not make his second-half strike any more special as he took his season's goal-tally into double figures.
After maintaining his record of finding the net in each round that Bradford have been involved in so far, he told BBC Sport: "Of course, I wanted to get a goal today but I wasn't thinking about having scored in every round.
"I was just pleased that our second goal gave us a little bit more of a cushion.
"My spell at Sunderland wasn't in my thoughts. The Sunderland support was fantastic, they stuck around to clap us off."
Bradford have little time to savour their success, as they return to league duty at Leyton Orient on Wednesday.
Phil Parkinson's Bantams side are in the thick of the play-off race, and victory could push them back into the top six.
Stead added: "We had a couple of minutes' celebration in the dressing room, but we've got the Orient game coming up this week so it's a quick turnaround.
"We're having to postpone league games because of our cup ties, but we're happy about that. It's been a fantastic effort from the lads."
Bradford FA Cup hero Jon Stead claimed the 2-0 victory over Sunderland was even better than their stunning win at Chelsea.