With a noticeable wind in the host's favour, stunning strikes from Peterborough duo Kgosi Ntlhe and Britt Assombalonga gave Posh the half time advantage at London Road.
A change in formation and the introduction of Andy Gray and Kyel Reid at the break brought the Bantams back into the contest for the second period though.
Aided by the windy conditions now working to their advantage, City looked a genuine threat in the second half, especially down the left flank thanks to the extremely lively Reid.
It was Reid who would act as provider for Gray to score and reduce the Bantams' arrears, but the effort, and the improved second half display, weren't quite enough to see City pick anything up from their first fixture of the festive period.
Parkinson said: "First half was difficult as we were against the elements. Their first goal is something you can do very little about when the lad hits it from that far out.
"The second goal, however, I felt we could have defended better against, so we gave ourselves an uphill task.
"The wind has definitely played a part in the game. It has helped with their first goal and it helped us in the second half.
"I just felt if we could have kept it down to one goal in the first half, we could have got something from the match.
"We've changed it around and made the substitutions at half-time, and I thought the lads who came on did great.
"We went back to 4-4-2 in the second half, but the conditions were also in our favour in that half as well
"Andy (Gray) held the ball up well and gave us a real platform to work with and (Kyel) Reidy was a real threat.
"We've had some good chances in that second half and we perhaps just needed a bit more conviction and belief on the ball when the opportunities fell our way.
"That was probably just the missing ingredient because the manner in which we played in the second half was excellent. The lads have to take a lot of credit for that.
"Obviously we are disappointed to lose, like you always are, but we have to dust ourselves down now and get ready for Boxing Day and Rotherham United."
Gray's second half strike at Peterborough was his first of the season and his first for the club since his return to the Coral Windows Stadium back in January.
With the injured James Hanson a doubt for Thursday's bumper Boxing Day clash with Rotherham United, Gray could now be in line for his first start of the season.
Parkinson added: "That (the goal) was an important one for him.
"He came back into the club for pre-season looking really fit but then unfortunately broke his arm at Guiseley, which was obviously a blow to him and to us.
"He's trained hard and looked good in the reserves since coming back, however, and I thought he did great today (Saturday).
"His all-round play was good and he gave us something to work with in attacking areas."
Before Gray and Reid's half-time introductions, Parkinson had set his side up to begin the game in a 3-5-2 formation, with Matt Taylor joining Matthew Bates and Rory McArdle in central defence.
Parkinson said: "We looked at Peterborough with their diamond shape in midfield, which can cause team problems, and we just felt it was the best way to go.
"Obviously after the game it looks like that wasn't the case because we were two goals down at half time. Whatever system you play though, I don't think you can do too much when someone smashes one in from distance like their full back has done.
"The second half improvement was a combination of the spirit and desire shown by the lads, the change in formation and the conditions being in our favour as well. Even if we would have stayed at three at the back for the second half though, I still think we would have had some joy with those conditions like we did at 4-4-2."
Phil Parkinson's full post-match Peterborough United interview can be viewed on Bantams Player by clicking HERE.