The Bantams have been rocked by the news that influential defender Andrew Davies has been ruled out for three to four months after undergoing knee surgery earlier this week.
With Rory McArdle and Carl McHugh away on international duty and Matt Taylor currently on loan at Colchester United, Davies' injury blow leaves City with only one available centre half - Luke Oliver - for their Sky Bet League 1 fixture with Tranmere Rovers.
Top scorer Nahki Wells will be another to miss out as well as he continues his recovery from a recent ankle problem.
Despite the sudden decimation of his defensive ranks though, Parkinson refuses to use the problem as an excuse heading into Sunday's date with Tranmere.
Instead, Parkinson will ask his players to raise their game just that little bit more to compensate for the loss of some of their team-mates.
With City's loyal support as vocal as ever last weekend at Walsall, the Bantams chief hopes the Bradford fans on Sunday can do the same to create a boisterous atmosphere around the Coral Windows Stadium.
Parkinson said: "With Andrew, it wasn't really until the Wednesday night when we knew that he would have to have an operation. Before then we had hoped we would still be able to manage the injury.
"It has been a tough week. To have four centre halves away from you is quite strange, but we are going to have to deal with it.
"We are going to ask the players who play on Sunday to give us that extra 5-10% more.
"We'd like to ask the supporters, if possible, to do the same.
"In football, sometimes you get some adversity come your way and that is when you need everyone to pull together.
"We need the fans to do their bit and really make it a cracking atmosphere on Sunday.
"The crowd were great at Walsall last weekend - the atmosphere they created there really was tremendous. We would love them to do the same again on Sunday and really make it a cracking 'cup tie' sort of atmosphere around the ground.
"Our players tend to thrive on that sort of thing.
"As I said before, we will be asking for that extra little bit on Sunday from the players, and the same goes for the supporters."
Despite City's serious defensive problems, Parkinson's men will still go into Sunday's clash as favourites after Tranmere fell to the foot of the League 1 table following last weekend's narrow loss at Swindon Town.
Parkinson isn't fooled for a second by Tranmere current position in the standings, however, and he feels neither should anyone else connected with City.
The Bantams boss added: "Tranmere come to us as a team at the bottom of the league.
"The minute we starting thinking we are just going to turn up and win though, that is when we won't.
"I've looked at their games and they have been competitive in every one of them really.
"They haven't been getting beat heavily. Last weekend at Swindon, for example, was a tight game for them, losing one-nil, so we have to respect them as they have some good players.
"Equally though, there has to be a certain lack of confidence in the team sitting bottom of the league, and we have to look to exploit that.
"As I say to the lads before every game, if Tranmere do come away with anything from the game come quarter to five on Sunday, we have to make sure that they have really had to earn it."