A single goal from Kyle Vassell just before the hour mark gave visitors Peterborough a narrow away win and consigned the Bantams to their first defeat in all competitions for the new 2014/2015 season.
The game saw nine minutes of injury time after the allotted ninety minutes due to a number of injury stoppages - including a suspected broken arm for Andrew Davies - during a bitty second period but Parkinson's men still couldn't quite find a way through.
Parkinson said: "I felt in the first half it was a good game of football and that we had played well, it was just our final ball that was letting us down.
"Second half was a bit more scrappy, however, something that obviously wasn't helped by the stoppages.
"I felt we lost our way a bit for a period in the second half as well, certainly in terms of the way we wanted to play.
"We got it back towards the end of the game and when we passed it through midfield using the likes of Billy Knott I felt we looked like we could create something.
"Unfortunately overall though, we just lacked that creative spark, that one killer pass, that one moment of quality to win us a game of football.
"It was always going to be a tough game today (Saturday). They are a decent side - we know that. The first goal was always going to be crucial.
"Peterborough obviously got it which lifted them and we found it difficult to respond.
"We said to the lads at half time that the game had that feeling about it. Two decent teams going toe-to-toe - we knew we had to try and stay in the game and stay strong with regards the shape of the team.
"We wanted that one moment in the game to come to us, unfortunately it came for them, and that allowed them to kill the game off.
"They slowed things down and wasted time, which was frustrating, but I suppose they are entitled to try and win the game in whatever way they see fit.
"You never want to lose in football but we've still had a good start to the season. We wanted to go into Wednesday (vs Leeds United) still unbeaten but we are happy with our points return so far.
"We will pick ourselves up after this defeat and look forward to what will be a cracking night here at the Coral Windows Stadium on Wednesday."