A goal in first half stoppage time from Gary Liddle was added to just before the hour mark by Billy Clarke to seal a comfortable home success at the Coral Windows Stadium for Parkinson's men.
After expressing his displeasure at certain aspects of City's play in the first period of their Emirates FA Cup tie at Aldershot Town last Sunday, Parkinson was buoyed to see his side right back on the money from minute one against the Railwaymen.
Parkinson said: "We had a lot of chances in the first half before eventually getting our goal from a set-play just before the break. It was another great delivery from Tony McMahon and Gary (Liddle) has shown great desire to get to the ball.
"That settled us all down, and then Billy Clarke's goal in the second half has really killed the game off for us. We probably could have scored more but you can't complain when you pick up a win and another clean sheet.
"I felt we lacked the desired intensity in our play for the first 45 minutes down at Aldershot last weekend. When you lose that desire and intensity from your team, it can be easy to look a very original side.
"Myself and Steve (Parkin) managed to show the lads some things during the week and those elements were right back in our team today (Saturday). We didn't take our foot off the gas for one minute.
"We closed them down, played with quality when we had the ball, and created numerous chances so I am really pleased with the way we played. We have to keep it going now and continue it into Wednesday and our replay with Aldershot."
City supporters can watch Bantams boss Phil Parkinson's FULL post-match interview with Bantams Player HD by clicking HERE