Billy Clarke's headed effort in the first period against Swindon Town on Saturday was enough to help move the Bantams' up into third place in the league table with their fourth straight 1-0 victory.
With Swindon playing with large numbers in midfield in the second half in particular, the visitors enjoyed large spells of possession after the break but City saw out the game in a professional manner.
The win certainly wasn't City's most dominant of the season so far but with games running out in the regular campaign, it is results that are the most crucial thing for Parkinson and his side.
The Bantams chief said: "You look at Burnley earlier in the day, they probably didn't play at their best but they got the win (1-0 at home to Leeds United).
"Everyone has been mentioning Leicester City recently, they have that ability to win those tight games. All games at this stage of the season are tight because every team is looking for those all-important results.
"We started the game really well. We did everything we had set out to do - we switched the play, got into some good crossing positions and forced a number of corners.
"We got the goal but then I thought we got a bit sloppy towards the back end of the first half. While they didn't threaten our goal too greatly, we probably gave them a bit of confidence by giving the ball away.
"Swindon made it difficult for us in the second half because they didn't play with a natural striker and we were overloaded in the middle of the pitch.
"It was difficult to get the ball back at times in that middle third of the pitch but the game is decided in the final third and I thought they never really troubled us.
"We had to be disciplined, concentrate and show good tactical awareness, and the lads all did that.
"It is about mentality, it is about determination, and it is about having an understanding of what is required. We have got ourselves in a good position with five games to do, and we will look forward to every one of them.
"The lads are ready for them."
The only downside on another successful afternoon for City was the sight of Kyel Reid limping off midway through the second period after appearing to take a kick on his ankle.
Parkinson is confident, however, the injury isn't anything too severe.
Parkinson added: "He got a cut on his ankle.
"We are not sure how bad it is but hopefully it won't be too serious and Reidy will be flying this week in training."