Phil Parkinson's men take on fellow League 2 side Burton Albion tomorrow (Tuesday) evening knowing that victory will take City to their furthest point in the competition since reaching the quarter-finals in the 1988/89 season.
Atkinson said: "It would obviously mean a lot to supporters if we could get through and it would mean just as much to us players.
"To be part of a side that achieved that for the club would be special indeed.
"We're in good form at the moment and we are really keen to continue that on.
"When you're on a winning run, you just want to play every game. There is no difference to the way we will approach this game. Cup tie or league game, we will be approaching this game like it's the most important one. It's our next one so it is (our most important)."
Like City, opponents Burton will head into the tie off the back of a four-game unbeaten streak after winning three and drawing one recently in the league.
To continue the similarities with the Bantams, while City were winning at Watford, Burton also booked place in the third round by picking up their own impressive away win at a Championship side - a 4-2 win at Leicester City.
Atkinson says that Parkinson will ensure that City are fully-prepared pre-match before they face up to their fellow in-form side this Tuesday.
"We'll leave no stone unturned in our preparations," Atkinson added.
"We will treat this match like we treat any other. We'll look at the opposition and try to work out their strengths and weaknesses.
"Burton are on a good run and have some real goalscorers in their side, but we've got to make sure we put on a performance worthy of getting us through."
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