A single Ryan Lowe goal just over twenty minutes from the end harshly consigned Parkinson's side to their first home defeat of the season this Sunday afternoon.
Although City weren't at their best for their latest League 1 encounter, Parkinson says he couldn't fault the endeavour and commitment of his players and felt the Bantams deserved at least a share of the spoils.
And while Parkinson was critical of certain aspects of City's play, he was, however, most annoyed by a number of refereeing decisions made throughout the contest, in particular the incident that saw Ian Goodison escape with only a yellow card despite the defender appearing to catch Kyel Reid in the face with his elbow midway through the first half.
The City chief said: "Regarding the incident in front of the dug-out (the Goodison elbow), I felt at the time that it was a straight red card. Having had the benefit of being able to watch it back again on the match DVD, I can say it is a definite straight red.
"The fourth official who I spoke with said that he (Goodison) didn't hit Kyel with his elbow, he just hit him with his forearm. If a forearm smash isn't a sending off then the fourth official has been watching a completely different game to the one I have watched over the last ten years.
"It was a big call, and they got it wrong."
Parkinson continued: "We also haven't had a penalty all season, and that is starting to concern me. You go back to a few weeks ago when Kyel Reid was clearly brought down in the box at Gillingham and didn't get a penalty. We had lots of moments today (Sunday) where you feel a penalty could have been given and we haven't had one. You would say that surely sooner rather than later we are going to get one.
"I went in to see the referee after the game and just said to him that I didn't feel he did enough to stop Tranmere from implementing their tactics of slowing the game down from the first whistle.
"There wasn't enough effort made to speed the game up.
"Our fans have paid good money to come to the game today. You can't blame Tranmere, they have come with a plan which they think will work for them. The officials have to make sure that sort of thing doesn't happen though.
"It wasn't until about seven or eight minutes to go before the referee started to respond to it even though everybody else in the ground had been able to see it clearly for a while.
"They weren't proactive enough in the way their officiated the game today.
"On the balance of play, we have definitely deserved something from the game. It was just at times we had to be patient on the ball because of the numbers Tranmere had back.
"We speak about playing with a high tempo and playing quick football, but there is also the other side of the game when teams have got men behind the ball and you have to be patient and pass well.
"At times we have done that well today, but our shooting from distance wasn't good enough. It was a greasy surface today because of the wet conditions - a great day for shooting low and letting the pitch quicken up the ball - but we haven't worked the 'keeper enough.
"We just couldn't find that moment of magic to get us through. Getting the first goal today would have been important for us because Tranmere came here with a 4-5-1 formation and sat back looking to make it really difficult for us.
"In terms of effort though, I don't think we could have asked anymore from the players today. They gave us everything.
"I am disappointed with the goal we have given away, however. It was a kick from their 'keeper, we've lost the first header and not got our covering positions right. We've let a very good striker free in our eighteen yard box and that shouldn't have happened. The goal gave them a huge lift."
New signing Matthew Bates was an unused substitute for the Tranmere fixture after signing a three-month deal with the Bantams. Bates comes into the club following Andrew Davies' recent knee surgery, although the versatile performer has also been brought in as cover in midfield as Ricky Ravenhill looks set to leave City on loan.
Explaining his decision to bring Bates to the Coral Windows Stadium, Parkinson said: "It's three-fold really. Obviously with Andrew getting his injury, he can help us in central defence.
"Matty can also play full back and he can play in midfield as well. Ricky Ravenhill has expressed his desire to go out on loan. He feels he is at an age where he needs to be playing regularly and I agree with him.
"I feel it is time for Ricky to move on and get some football, so Matt covers us in midfield in Ricky's place. He covers us at right back as well, along with his favourite position of centre back."
With Bates on the bench, Parkinson decide to partner Nathan Doyle with Luke Oliver in central defence following the club's recent defensive problems.
Parkinson said: "We went with Doyley (Nathan Doyle) because we knew we would have a lot of the ball as I expected Tranmere to play with only one up front.
"In that scenario, your two centre backs are going to have a lot of the ball, and Doyley, in particular, is a good user of the ball."
The move to put Doyle back into defence meant Parkinson handed Jason Kennedy his first league start for the club following his summer move to Valley Parade.
Parkinson added: "I thought Jason worked really hard today.
"He put in a good performance. He was committed, he was strong and he passed it well."
Carl McHugh was back at Valley Parade to make up part of City's list of substitutes after being given permission to temporarily leave the Republic of Ireland Under 21s camp.
The young defender will now join back up with the under 21s squad ahead of their match with Romania in Sligo this Tuesday afternoon.
Parkinson added: "We didn't have any cover for left back on the bench without Carl, so the Irish F.A kindly let have him back for today so we could have him on our bench."