But he insisted it "wasn't a hard luck story" and accepted their promotion-chasing hosts had played a full part in an entertaining game that deserved goals.
Parkinson said: "The lads were outstanding and in the second-half we really took the game to them. On another night James Hanson could have scored a couple of goals and there were scrambles in their goal-mouth when I don't know how the ball didn't go in the net.
"I thought the spirit, energy and quality in our play was terrific and I couldn't have asked for anything more from them. We've gone three unbeaten now since Wembley, including two clean sheets away from home, and that's good going.
"We got out to try and win every game and we made attacking substitutions in the second-half to try to get the three points.
"But we shouldn't forget Jon McLaughlin has made a world-class save from Tom Pope in the first-half and Vale also had a chance or two towards the end."
Vale, with Darren Purse a tower of strength at the back, at least held out for an important point, although skipper Doug Loft was sent off in injury-time for a high challenge on Ricky Ravenhill.
Vale's cushion above the chasing pack has been eroded away with a run of five points from six games with only two goals scored.
"There were crumbs of comfort and we will take them and move on," manager Micky Adams said. "I was pleased with the effort and commitment of the players. To a man they stuck to the task and we went toe-to-toe against a very good Bradford side.
"I want to see the sending off on the tape before I comment, but I've been to see the referee and he says Doug went over the top of the ball."