With only eleven minutes of normal time left at windy and rainy Greenhous Meadow, Parkinson's men found themselves in the lead when Andrew Davies swooped from close range to convert Matthew Dolan's teasing cross.
Crucially, however, City's new-found advantage would only last barely thirty seconds as the hosts equalised with their first attack after the restart through Jon Taylor.
Worse was still to follow for the Bantams as they conceded Shrewsbury's winner from Shaun Miller in the final seconds of injury time with one of the last kicks of the game.
Understandably, both goals caused immense frustration for Parkinson as the Bantams turned a possible hard-fought victory into a disappointing defeat in the final stages of the match.
Parkinson said: "I'm bitterly disappointed.
"Conceding so quickly after scoring ourselves was hugely frustrating - we've just switched off and got punished for it.
"At one-nil to us, obviously you are thinking and hoping that we can go on and secure the win.
"To end up getting beaten two-one then is really, really disappointing for us.
"At one-one, a point wouldn't have been the worst situation for us to come away with, especially with the windy conditions.
"To lose the game after being one-nil up so late on is a real blow.
"We gave the ball away too cheaply at times towards the end of the game and gave them a lift. We were too careless in possession.
"The weather conditions did dictate the game a bit today (Saturday). I was pleased to get in nil-nil at half time because the elements were against us in the first half.
"We said to the players at half time that we were kicking with the wind in the second and kicking towards our supporters and we needed to sustain some real pressure.
"Did we do that enough? Probably not.
"The main period in the half that we did do that, however, we got our goal from it.
"The game was always going to be a scrappy one given the conditions, but it was the sort of game where it was a case of get the job done, win your battles and get back on the coach with the win. Unfortunately we've not done that."