Ten days after their goalless draw in the original first round tie, City and Aldershot will meet up again at the Coral Windows Stadium in front of the BT Sport cameras for their televised replay.
The Bantams will come into the match following a 2-0 home success over Crewe Alexandra at the weekend - a result that stretched their unbeaten league run to seven games.
The victory also made it three wins and a draw from City's last four home games, and Parkinson is aware that the Bantams will have to show all of that recent match-winning form on Wednesday night if they want to finally overcome the challenge of Aldershot.
Parkinson said: "As we fully expected, the first match down at Aldershot was a really tough game.
"Aldershot are a well-organised side and full-time team in their division, and results have proven this season that cup ties against conference clubs are not easy by any stretch of the imagination.
"We know we will be in for another competitive match on Wednesday but we will be doing all we can to make sure it is our name going into the second round.
"We were disappointing in the first half (of the original tie) but we improved in the second half.
"After a pleasing result on Saturday (vs Crewe Alexandra), it is important that we continue to maintain the high standards we have set in recent weeks when we kick off on Wednesday night."