After collecting only a draw and a defeat on the road in recent games despite two strong performances, Parkinson knew that victory against the Saddlers was important for City's hopes of securing a Play-Off place.
With the Bantams chief calling pre-match for City to rise to the occasion, his players responded emphatically with a thumping win in front of a vocal home support against a side who still have hopes of gaining automatic promotion.
Parkinson said: "Getting only one point from our last two games added some pressure to this game, not to mention playing against a side pushing for automatic promotion in front of one of the biggest crowds of the season.
"What pleased me most from today (Saturday) is the way we have handled the occasion.
"We've put in arguably our best performance of the season at home when we've needed it the most. That bodes well for our next games.
"The players love playing at this ground. The atmosphere was fantastic again.
"If you can't enjoy playing in front of our supporters, then you are in the wrong sport because the atmosphere was tremendous. I am so pleased we have sent them home happy this evening.
"I'm sure the fans will be like us though, not looking too far ahead and just looking forward to Southend next weekend.
"We have had periods in recent weeks where we looked certain for the Play-Offs, then things tightened back up again, so that is why today was so important.
"We have to go to Southend and play at our very best in another huge game. After today, the lads can't wait for it."
Following a goalless first period, City registered four unanswered goals thanks to an opener from Filipe Morais on his first start of the season and a sixteen-minute hat-trick from James Hanson.
After nine games starting from the bench, Hanson was recalled into the attack to lead the line just ahead of Morais, who was given license to support City's top-scorer in a 'number ten' role.
Parkinson added: "Time and time again for us, James has shown he has it in him to produce in the big moments, and he's got three of them today.
"His overall play was excellent. He has took it like a man being out of the team, he has waited patiently for his chance and we just felt he was ready to get back into the side today.
"He has certainly repaid that faith in him.
"It is similar with Fil (Morais) really. We just felt we needed a spark in attack and that Fil would give us that.
"Looking at training this week, he looked like a player that we needed in the team.
"We hoped his quality and his enthusiasm would give us a lift, and it did.
"There is always a bit of a gamble involved playing a player in a different position but he has played in attack before for Stevenage.
"When you consider that was his first start of the season, that was a remarkable display from him."
The only downside on an extremely positive afternoon for Parkinson's side was the sight of Reece Burke leaving the pitch early due to a hamstring injury.
Parkinson added: "His hamstring was a bit tight.
"To be fair to Reece, he had a problem with his calf leading up to this game but he was adamant that he was going to play.
"We will have a look at him this week but hopefully it isn't serious."