A first half penalty from Alan Sheehan, plus two goals from Billy Clarke and a late strike from Raffaele De Vita, secured Parkinson's men a comfortable 4-0 victory on the final day of their week-long stay in Ireland.
With City continuing to use a 'diamond-shaped' midfield four - this time with Gary Liddle just in front of the back four and Mark Yeates supporting the front two - there was plenty of slick passing and smart inter-play on show from the Bantams at Tolka Park.
Parkinson said: "We have to be really pleased with our week here.
"The facilities we've been using have been superb and the lads have got a lot out of the week.
"There was some tired legs out there today (Saturday) because the lads have training really hard.
"As you would expect, we have been pushing the lads hard this week with it being pre-season and they have really responded to what we have asked of them.
"Today was a decent workout for us. We've worked the ball well and scored some good goals.
"Pre-season is a lot to do about fitness but gaining confidence from scoring goals and winning games is also important."
Reflecting on City's 4-0 Shelbourne win, Parkinson made a point of praising the performances of two of his summer signings in particular.
Along with his two goals in the game - his first in City colours - Irish striker Clarke caught the eye with his link up play being the Bantams' midfield in attack.
At the other end of the pitch, Liddle cut an imposing figure as City's protector of the back four in their midfield diamond.
Parkinson added: "When you come to a new club, you want to get off and running as soon as possible whether it be a league game or a pre-season game.
"Because of that, I was really pleased to see Billy get his two goals.
"They were two great goals. The first one was an excellent finish and the second is a really good strike from distance. To get two in this match is a nice little bonus for him and for us.
"His all-round performance was good today and he needs to take a lot of credit for it. Billy is the sort of player where we can get the ball into his feet in and around the box and he will make things happen for us.
"I know Gary Liddle did excellent for us in that holding role.
"He is very, very good at that - he didn't give the ball away.
"He picked up the right positions when the opposition had the ball. I felt he did excellent today."