A close encounter at the Coral Windows Stadium was settled thanks to a well-taken finish from close range by substitute Steven Davies barely seconds after coming on the pitch midway through the second period.
The victory was City's third on the trot and the fifth in their last six games, while the deserved clean-sheet to go with the victory was incredibly the Bantams' twenty-third of the season so far.
Parkinson said: "We know Scunthorpe are a good side - they were on a long unbeaten run before today (Saturday) and they came here on the back of a 6-0 victory - so we knew it would be difficult.
"I felt in the first half we were a little bit below our levels but there were reasons for that.
"If you look across the midfield, Tony McMahon played with an injection in his right toe, Kyel Reid has only trained once this week due to a chest infection, Josh (Cullen) has been troubled with a thigh problem recently and (Lee) Evo didn't get back into the country until Wednesday because of international duty.
"We spent a long time thinking over the team selection for this game. We've have a lot of good players who didn't even make the bench today, it was also hard to leave out Billy Knott and Tom Thorpe after the way they played over Easter.
"What pleased me a lot was that we were still very much in the match at half time despite not quite being at our best. (Stephen) Darbs has produced two tremendous goal-line blocks to stop them scoring and we've shown some real determination not to concede.
"If you haven't played at your best and you come in at half time a couple of goals down, you can find yourself with a bit of a task but we kept ourselves in the game at the break. The way we then lifted ourselves for that second period was all about character."
Davies' match-winning goal amazingly came via his first touch of the ball after coming on as part of a double substitution made by Parkinson which saw the Liverpudian and James Hanson replace fellow strikers Billy Clarke and Jamie Proctor for the third fixture running.
Going into the game, Davies had unfortunately missed a sizeable chunk of City's training schedule this week due to a health problem affecting his daugther.
Parkinson added: "I am very pleased for Steven. He has missed a bit of training because his daughter has been in hospital this week. We understand she is making good progress but it has still meant he has missed a lot of the week.
"It hasn't been ideal for him then but what a player for us to be able to bring on when you are trying to win a match.
"He is playing with confidence at the moment - that's a fifth goal off the bench for him now - and the crowd are really warming to him."
On another pleasing day for Parkinson's men, one of the biggest cheers of the afternoon was reserved for the return of the fit-again Filipe Morais.
The popular Portuguese winger was introduced into the action with seven minutes of normal time remaining for his involvement with City's first team since seriously injuring his knee in pre-season training last summer.
Parkinson said: "It was great to see him out there. He looks fit and he has a real enthusiasm for the game - he is determined to play a part this season.
"I remember the day he got injured in pre-season, we were all low because we knew what a blow it was to lose a player of his talent.
"We are certainly pleased to have him back now though."
The win over Scunthorpe moves City up to fifth in the League 1 table and level on points with fourth-placed Gillingham but Parkinson maintains that the Bantams musn't focus on anything over than their next opponent.
Parkinson added: "It is important that we keep our feet on the ground.
"I say it every week, but we all know about the tight nature of this division. We saw another example of that today with Scunthorpe and how well they played at times.
"If we start thinking we are better than we are or we get carried away with ourselves and we come down 5 or 10%, that can be enough to not get those victories.
"We know we have a good team and a good squad but we are only capable of winning games when we play flat out.
"The lads have given the club absolutely everything this afternoon and that is very pleasing."