Tuesday's narrow home loss at the hands of Barnsley was all the more frustrating for those in the Bantams camp due to the fact that Parkinson's men had arguably played well enough to at least pick something up from the match.
With Mark Marshall and Josh Morris in particular looking threatening on the flanks, City found themselves in a number of promising opportunities throughout the ninety minutes against the Tykes but they were unable to quite engineer a vital breakthrough.
The Bantams now have the task of making those chances count when Fleetwood arrive at Valley Parade at the weekend, and Parkinson knows that the fans, as always, can play their part in pushing his side on.
Parkinson said: "We know we are going through a difficult period at the moment. But the bravery shown by the players to keep doing the right things on the ball, and the support shown by the fans all the way through Tuesday night, gives us great heart going into the weekend.
"We will stay strong as a group, as we always have done, and come through this spell.
"We have always prided ourselves on having real character within our group, and our mentality is as strong as ever.
"As I mentioned in the press after Tuesday's game, the supporters were terrific right throughout the game and really stuck with the lads.
"I would ask them to stick with the lads again on Saturday and together let's see if we can get things going again."
After coming off in the second half of the Barnsley game, Billy Clarke is expected to miss the next couple of weeks with a hamstring strain.
Reece Burke, who also limped out of the Tuesday's match, will have a scan on his Achilles injury today (Thursday) while Stephen Darby and James Meredith are being monitored after picking up knocks in the same fixture.