In their first game of 2016, Parkinson's men found themselves two goals down after only eleven minutes thanks to early strikes from Gillingham duo Bradley Dack and Rory Donnelly.
It could have been worse for the Bantams but Stephen Darby was on hand to head clear off the line from Donnelly barely a minute or so after the striker had doubled the Gills' advantage.
Thereafter, City had a number of chances to wrestle themselves back into the game - with the recalled Devante Cole going close more than once and Reece Burke and Rory McArdle seeing efforts blocked on the goal-line from one Tony McMahon corner delivery.
City couldn't turn their opportunities into goals unfortunately though, and Gillingham substitute Doug Loft was on hand to seal the points for the hosts when he converted Ryan Jackson's cross shortly before the end of normal time.
Parkinson said: "We were second best at the start of the game and we got punished for it, and that is not good enough and not acceptable.
"At two-nil down, we've had chances in the game but it is a bit too late to start playing then.
"We've had some great opportunities to score but we have to do better, we have to make the 'keeper work.
"When the pressure was on and it was a physical start from Gillingham, we weren't good enough. We were too soft all over the pitch.
"Bradley Dack has produced a moment of quality at the start of the match and that has lifted his side.
"We need our attacking players to take their chances when they come along.
"We have also gone from a team that didn't look like conceding to a side who have let in six goals in two games.
"We need to look at that and get back to where we were before because we have become a bit soft at the moment. We need to show character and stand up to be counted.
"I am not happy with the players and I am not happy with myself and we need some straight talking this week at the training ground."
Along with Cole, James Meredith and Billy Knott were also brought back into the side for the Priestfield Stadium encounter.
Knott was added to City's midfield with Lee Evans set to return to parent club Wolverhampton Wanderers.
Parkinson added: "Greg (Leigh) has done tremendously for us recently but I just felt it was the right time to bring Mez (James Meredith) back into the side.
"With Devante's pace, we felt he could have caused them problems. He's had chances in the game and on another day he could have scored a couple of goals.
"I spoke with Wolves this week and they explained that they wanted to bring Evo (Lee Evans) back to have a look at him for a couple of weeks when his loan finished next Saturday (9 January 2016).
"We wanted to keep that away from him so he could focus on this game. When he was told he was going back, however, we felt it was probably best to give the players who are going to be here a chance.
"Some of those players haven't taken that opportunity though."
On a difficult day for the Bantams, City lost Reece Burke to injury early after the restart and Nathan Clarke was dismissed in injury time.
Burke was sent to hospital for checks to see whether he had broken his right wrist after suffering a deep cut to the area when he crashed into the sponsor-hoardings while challenging for the ball by the near touchline.
Clarke - Burke's second half replacement - was given a straight red card for tugging back Gills substitute Elliot List as the striker looked to race clear on Ben Williams' goal.
Given the nature of his dismissal, Clarke is expected to be given a one-match ban, meaning he will miss next Saturday's trip to Bury in the Emirates FA Cup third round.
Parkinson said: "Sometimes you get days when you think 'can anything else go wrong?'. We've had one of those days today.
"Reece has been outstanding for us but it looks like he has picked up a serious wrist injury.
"He has gone for checks at the hospital to see exactly how bad it is.
"Nathan Clarke getting sent off at the end as well makes it a very journey back for us."
The trip to Gillingham - the Bantams' twenty-third game of a forty-six game season - marked the halfway point in City's 2015/2016 League 1 campaign.
Clearly disappointed by the manner of City's defeat at Gillingham, Parkinson says that a lot of important decisions will need to be made in the coming weeks to try and ensure the club's second part of the season is a successful one.
Parkinson said: "We have another half of the season to go, and we know we have the capabilities of going on a good run.
"But I think a day like today makes us want to reevaluate how we want to go with things over the next few weeks.
"We have become too open and not physical enough at the moment.
"When we come up against a side like Gillingham who start strongly - we showed the players what to expect in the hotel last (Friday) night - and they don't respond to that, I have to address that."