Despite matching their hosts for long periods of the game, a fortunate Danny Kedwell double helped Gillingham on the way to their first points of the new campaign.
Kedwell's first - an unorthodox flick for goal that somehow nestled into the corner via the far post when it seemed like the striker was trying to cross - gave the Gills the lead just before half time.
A soft penalty decision when Charlie Lee went down in the box over Will Atkinson's leg then allowed Kedwell to expertly rifle home his second from the spot early into the second period.
Substitute Nahki Wells deservedly got City back in the game, however, just past the hour mark when he won and then scored City's own spot-kick.
Parkinson's men pushed forward for an equaliser - with the Bantams boss pushing Andrew Davies into attack and playing three at the back at one point - but Myles Weston eventually put the game beyond City with a fine late strike.
"I think on the balance of play we deserved something from the game today," said Parkinson.
"I thought there were some positive aspects to our play, I was just particularly disappointed by the second goal.
"We switched off as a team and ended up giving a penalty away.
"(Coming from) Two nil down, as we were after the penalty, was always going to be tough. But credit to the lads, we had a real go.
"We got the goal back, and at that stage I really felt that we were going to be the ones getting the next one.
"We had a few moments where we maybe could of done if we'd done certain things slightly better.
"Eight minutes to go, I've made the change to go to three at the back and have a bit of a go at it. That is always going to leave you a bit exposed defensively and ended up getting caught for their third on the counter-attack.
"The third goal - I'll hold my hands up for that one. At two-one down, you have to go for it with time running out. I just felt that Davies' aerial presence would cause problems up there.
"All in all, there were some good things to take from today but obviously we''ll go home very disappointed to lose because we all want to win games here. I believe on the balance of play we should have got something."
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