City were good value for the half time lead they held thanks to Aaron Mclean's first goal for the club but a sloppy goal conceded by Parkinson's men just over ten minutes into the second period helped the visitors to snatch a share of the spoils.
Given the Bantams' positive play during the Gillingham fixture, especially in the first period, Parkinson couldn't help but feel that City should have secured victory from their encounter with former boss Peter Taylor.
City's current chief was at least pleased, however, to see some of the bright play that helped to pick up the win at Colchester United Tuesday continue on into this weekend's contest.
Parkinson said: "The game panned out as I thought it might do at times.
"Gillingham sat back and let us have the ball and I thought we moved it about great, especially in the first half. Some of the play was excellent. It certainly warranted more than the one goal we got.
"Over the ninety minutes, we have dominated for large parts. When you have that possession and pressure though, you need to capitalise on that with more goals.
"We didn't get them though, and the goal we conceded was obviously a soft one.
"The ball has bounced over Andrew's (Davies) head and two or three touches later, it has ended up in the back of our net.
"We know we should have done better.
"(Adebayo) Akinfenwa and (Cody) McDonald are a good partnership and they offer Gillingham an attacking threat.
"McDonald scored a similar goal last year here for Gillingham in a similar sort of game.
"We are disappointed by the manner of their goal and that fact that we couldn't get a second one ourselves but there were many positives to take from today (Saturday) in terms of our general play.
"We carried on some of the good things from Tuesday night (vs Colchester) and some of our football was excellent.
"We know today is two points dropped in terms of the balance of the game but it is also another point closer to where we want to be.
"We know the games in this division are usually tight and you have to work really hard for everything. Today was no different - we've made one mistake and been punished for it."
After missing the Colchester win in midweek due to illness, club skipper Gary Jones returned to the side as a second half substitute.
With Jones starting the game from the bench, Parkinson elected to keep Matthew Dolan and Nathan Doyle together as City's central midfield pairing.
Parkinson said: "We are still actually awaiting the results of the tests we did on Gary but he felt fitter and sharper today. He looked a lot brighter in himself. It was good to have him back.
"Looking at it, he has probably ran himself into the ground with his efforts to get us some points over these last few weeks. His body probably just needed a break, and he's had that now.
"I thought Matty (Dolan) and (Nathan) Doyley used the ball really well. They both have the ability to switch the ball quickly, which is important when teams sit off you."