With Crawley being the third of three back-to-back away matches for City in recent days, Parkinson's side head into Tuesday's contest having already picked up a cup win, a league point and two successive clean sheets from their previous two games on the road.
Last Saturday's goalless draw at Walsall maintained City's early unbeaten start to the season following the Morecambe cup victory and the opening day defeat of Coventry City.
Opponents Crawley have gone one better, however, having won all three of their opening league and cup matches. With that in mind then, Parkinson knows the Bantams will have to be on their mettle come game time this Tuesday.
Parkinson said: "It was good to get back on the bus home to Walsall on Saturday with a hard-earned point in the pocket.
"For all of Walsall's possession at times, we looked strong and solid as a unit and difficult to break down. Jordan (Pickford) has only really had the save at the end from Adam Chambers to make during the game.
"We now have to show the same qualities we showed on Saturday and against Morecambe last week when we go down to Crawley.
"We know it is going to be a challenging fixture because, like us, Crawley have had a good start to the season.
"After our Walsall performance, we now have to go again and show the same discipline and determination at Crawley."