Parkinson's men twice came from behind at the weekend by scoring three times after the interval to earn a point against their Cheshire visitors.
After a lacklustre opening period, City's improved second half display saw the Bantams go close on several other occasions as well, with debutant Matthew Dolan and James Hanson on the end of promising scoring opportunities after the restart.
Encouraged by what he saw following the half-time break, Parkinson now wants City to continue their 'positive' brand of football up at Carlisle's Brunton Park on Tuesday evening.
Parkinson said: "After the way we played in the second half on Saturday, we go into Tuesday's game with our tails up.
"We have to make sure we play in that manner for the whole 90 plus minutes though.
"There was a big contrast between the first half and the second half on Saturday.
"We have to produce the second forty-five minutes for ninety minutes on Tuesday now.
"If we do that, we'll have a great chance of picking up the result we're after.
"Even being conservative, you could see that we could have scored at least a couple more than we did in the second half on Saturday.
"The attacking football we showed in that half would have given any team in this division problems.
"We know that some of the new lads are bedding in still. We sat the lads down today (Monday) before training and went through the good and bad points of Saturday and reminded them of how we play.
"We showed them why the second half was so much better than the first.
"The conditions on Saturday will have played a part, but there was definitely a different level of positivity to our play in the second half.
"In football, your first thought should be 'can I be positive?, can I pass forward?, can I run forward?'.
"In the first half, our first thought didn't seem to be that."
With Tuesday's trip to Carlisle coming just three days after Saturday's action-packed draw with Crewe Alexandra, and only four days in advance of an away fixture with Coventry City, Parkinson acknowledges that the thought of making changes to his starting eleven has crossed his mind.
When asked about the prospect of alterations, Parkinson said: "That is possible. We will look at a few things.
"We haven't named the team this (Monday) morning - we just worked on a few things in training regarding our play.
"We have hedged our bets slightly in terms of the personnel - it gives us just another twenty-four hours to check everybody."