James Hanson's 94th minute winner capped a thrilling second half fightback for Parkinson's side after they had found themselves behind to Shrewsbury with less than two minutes played.
The Bantams had to wrestle their way back into the match after the restart without the services of top scorer Nahki Wells, however, who limped off midway into the first period after taking a whack to his ankle.
Parkinson is hopeful the injury doesn't prove to be too serious, but the City chief says he will most likely have the full picture by the time his squad regroup for training on Monday morning.
Parkinson said: "We think it shouldn't be too serious for Nahki but we won't know for sure until tomorrow (Sunday).
"Matty (Head Physio Matt Barrass) has padded him up and got the ice on it. Once things have settled down, we should know more tomorrow."
Mark Yeates came off the bench to replace Wells in the Shrewsbury contest, with the Irish attacker given a free role next to Hanson up front.
Parkinson added: "Nahki has played a big part for us for quite a while now, but when he isn't playing, other players have to step up.
"Mark added a different dimension to the team when he came on. His clever play helped us and I felt he got more influential as the game wore on."