After two long away trips, last week saw Parkinson's men suffer narrow defeats at the hands of Swindon Town and Peterborough United.
With the Bantams now back on home soil, however, this Tuesday, Parkinson hopes his side can use the Crawley game as an opportunity to keep pace with League 1's fellow Play-Off contenders.
Parkinson said: "Our recent results haven't been as favourable as we would have liked and we'll be looking to bounce back with a positive performance on Tuesday.
"We go into the Crawley fixture aiming to stay in touch with the sides currently in the top six.
"With that in mind, we'll be doing all we can to get the right result on Tuesday."
Following the return of Andrew Davies at Peterborough United on Saturday after a recent hamstring injury, Parkinson expects James Hanson to be fit for the Crawley match after his own hamstring problem.
Gary MacKenzie should also be fit after a sore knee kept him out of the Peterborough game.
Filipe Morais, who has been sidelined with a knee injury, isn't likely for Tuesday night though.
Parkinson admits City are thinking more about trying, if possible, to get the Portuguese winger ready for Saturday's eagerly-anticipated F.A Cup Quarter Final with Reading.
Parkinson added: "Fil is doing well. He is a bit behind where Hans (James Hanson) is in terms of his recovery but he is improving.
"We've had the knee scanned and it is nothing too serious. It is still going to be touch and go for him for Saturday though.
"Fil is determined to make the game so we'll have to wait."
Gary Liddle is also out of the game as he serves out the last of his two-match suspension.
Opponents Crawley will come into the game in the League 1 relegation zone but with some impressive recent results under their belts.
After thrashing Barnsley at the Checkatrade.com Stadium and winning at Swindon Town, Crawley drew 1-1 at home to Sheffield United last Saturday.
Following John Gregory's decision to step down in late December due to health reasons, Crawley are currently led by former Bantams striker Dean Saunders.
Saunders, who spent two seasons in total at Valley Parade, scored City's first ever Premier League goal in the club's win at Middlesbrough on the opening day of the 1999/2000 season.