Goals from Kevin McDonald and Nouha Dicko secured the points at Molineux for Kenny Jackett's upwardly-mobile team, although Adam Reach and Stephen Darby both hit the woodwork for City.
With promotion hopefuls Wolves currently boasting a starting eleven that wouldn't look out of place in the Championship and the Bantams having to play with ten men for over an hour following Nathan Doyle's dismissal, Parkinson's men can take some solace from their disciplined defensive display.
The City chief was certainly impressed with the defending and work-rate on show from his players throughout this Saturday's contest.
Parkinson said: "The lads gave us everything today (Saturday).
"It was a tremendously-spirited performance considering we had to play away at one of the strongest sides in the division with ten men for over an hour.
"If we could have just got to half-time at 0-0, the game could have been different. The goal knocked us for six unfortunately.
"We lifted the boys again at half-time, however, and we told them that we would try to keep it tight at the start of the second half and then have a go towards the back end of the game.
"Once we have conceded the second though, we had a lot of tired legs out there and we had to make sure didn't we leave ourselves too exposed and concede a third or a fourth goal.
"Some of the performances from our lads at the back were outstanding.
"Stephen Darby was top draw today, as he normally is really, and the two centre backs (Carl McHugh and Rory McArdle) were great as well despite being up against a strike-pairing which has just cost Wolves over a million.
"Carlo (McHugh) came into the side and gave us everything - I thought his performance was excellent - and (Matthew) Batesy playing out of position again at left back was tremendous.
"The midfield protection was good as well. They gave good coverage to the full backs.
"The work ethic from (Adam) Reachy, Jonah (Gary Jones), young Chris (Atkinson) when he came on and (Garry Thompson) Thommo was excellent."
McHugh was brought into City's starting eleven to replace Andrew Davies as City continue to ease the centre half back into the first team scene following four months out with a knee injury.
James Hanson also missed the game with a minor hamstring problem. Hanson's place in the side was taken by Andy Gray.
Parkinson explained: "With Davo (Andrew Davies), he did great to play Tuesday but, realistically, playing him today so soon after would have probably put him at risk. We weren't prepared to do that.
"James has a nerve problem which is affecting his hamstring. It is not a muscle injury.
"The specialist looked at it and said that he could play today but there would be an increased risk of him tearing the hamstring.
"With that in mind, we decided to be cautious, and I felt that was the right thing to do bearing in mind the run of games we have coming up.
"Andy (Gray) has come in and done well in his place. He held up the ball well and gave good account of himself considering he hasn't played much football this year for one reason or another."