Less than five minutes after coming on, second half substitute Mark Yeates was on hand to cancel out Gary Liddle's opener for County and secure a point for Parkinson's men in the process.
Although not keen to use it as an excuse, Parkinson's preparations for the game were hampered by a sickness bug that had hit a number of his players over the last few days.
Six players in total - Rory McArdle, Matt Taylor, James Hanson, Alan Connell, Kyel Reid and Nahki Wells - were affected by the virus in the build up to the visit of Notts County.
Taylor was judged not fit enough even for the bench, while Wells had to be taken off just after City's equaliser roughly twenty minutes from the end.
Reflecting on the game itself, Parkinson felt his side had created enough chances to win the game but, given the disruptions of the last couple of days, the City chief was able to some comfort in the Bantams' second half comeback.
Parkinson said: "In the end, it is probably a good point for us.
"After going a goal down and in light of the recent sickness bug that has been going round over the last forty-eight hours, we have to be glad to at least pick something up.
"Having said that though, we've had more than enough chances in the game to win it.
"Even in the first half, where I didn't feel we played with enough positivity on the ball, we still had some good chances.
"Their goal as well is a poor one for us. We've given away possession cheaply while deep inside their own half. Although they still have to travel a long way to score, it was a poor goal.
"We're responded great in the second half, however. We've pinned them in and had chance after chance."
Parkinson continued: "Nahki was ill yesterday (Monday). Hans, Reidy, Matty Taylor, Alan Connell and Rory McArdle all had a strain of it as well.
"To be fair to the lads though, even Matty Taylor, who had been up all night and hadn't eaten all day, still turned up and said he wanted to be involved.
"You have to give them all immense credit for that.
"I've been in situations before in football where three or four players simply don't turn up because they have been feeling unwell, but all of our lads wanted to play.
"Myself and Steve (Parkin) were still thinking about what players to include even just before the game tonight, but it is not an excuse from us.
"As a player, you can't use that as an excuse once you put yourself up for selection and you go out there on the pitch.
"Of the players who made the full ninety minutes, Hanson was probably the one most doubtful to start in the first place but he, like the rest of the lads, kept going until the end."
For Yeates, his point-earning strike was his second goal of the season and an example, Parkinson reckons, of what the winger brings to the table for the Bantams.
Parkinson said: "We know Yeatesy has class and he has quality. He has that ability to produce that moment of magic in the final third.
"When he is either crossing the ball or having an attempt on goal, you always believe there is a very strong chance something will happen from it.
"He is angry at the moment because he is not in the team. He's angry, but in the right way. He is fired up to get back into this team, and I want him to be like that.
"As a player, all you can do is take your opportunity when it comes around. He has certainly done that tonight (Tuesday)."
After netting the winner at MK Dons last Saturday, Jason Kennedy was taken off at half time for Nathan Doyle in a tactical switch.
Parkinson explained: "Jason was very unfortunate.
"He played so well for us on Saturday but I just felt the way the game was going with their big number 4 (Liddle) sitting in front of Hanson, it left us a lot of space in central midfield to pass it.
"Doyley came on and made big difference in terms of getting our foot on the ball."
With City's next Sky Bet League 1 fixture at Oldham Athletic scheduled for this Sunday, Parkinson has taken the decision to keep all of his squad away from the training ground for the next two days - Wednesday and Thursday - in an attempt to finally get rid of the club's recent stomach bug.
Parkinson added: "We're going to shut the building (training ground) down for the next couple of days.
"We were going to be in tomorrow (Wednesday), but we've decided just to keep everyone at home, sterilize the training ground and hopefully everyone will be in good health for training Friday/Saturday."