After conceding an early wind-assisted free-kick goal from Jimmy Ryan, City earned a share of the spoils with a third goal of the season from James Hanson later in the first half at Highbury Stadium.
With City on top for long periods of the second half, Devante Cole twice went close to firing Bradford into the lead - heading narrowly wide with one effort before hitting the post eleven minutes later.
The Bantams thought they had snatched a dramatic late lead with virtually the last action of the game but Steven Davies' close range finish from a Lee Evans free-kick was ruled out for offside.
Parkinson said: "On the balance of play and looking back at the chances, we should be talking about three points from this game.
"We started slowly and perhaps got caught on the back foot a bit.
"They had two big six-foot plus strikers up there and they (Fleetwood) played to their strengths, which wasn't the easiest to deal with early on in the windy conditions.
"After that though, our response was excellent.
"The reaction after conceding the goal and our overall play after the slow start was very pleasing.
"The chances we created as well, plus the fact the subs have come on today (Saturday) and made an impact, there was plenty of positive aspects to take from the game."