First half goals from James Henry and Richard Stearman secured all three points for Wolves, but Parkinson's side could feel unlucky not have collected something from the game after having the better of proceedings during the earlier stages of the first period and for most of the second half.
Although naturally disappointed to lose out in such a keenly-contested affair, Parkinson acknowledged afterwards that he couldn't really have asked much more from his players against the West Midlands giants.
Parkinson said: "I felt we should have definitely got something out of the game.
"We have played really well in the second half and pinned them in for the majority of the half. Wolves are a good side - they have immense quality going forward - but we still deserved something from the game.
"I don't think we could have demanded too much more from the players today (Saturday).
"We started the game in a positive fashion and it is only after we have scored that Wolves have reacted and put us on the back foot. We are disappointed with the goals, especially the first one. Jonny (McLaughlin) has to really save it, but, in fairness to Jon, he has made some tremendous saves for us already this season.
"For 75% of the game, I felt we have played really well. We have produced so many good things against a good side - but we have still come away with no result to show for it.
"We have some good points to take away from today though. We know if we play like that next week, we'll give ourselves a good chance of getting a positive result.
"It is never nice to lose in anything - you always want to be on the winning side - but we have done everything in our power today to get back into the game.
"We said to the lads that we were going to approach the game like a cup tie because we knew the atmosphere would be like a cup tie.
"When you have lost in the manner we have done today, you can hold your head up high."
Before Henry and Stearman's goals for Wolves around the half hour mark, Raffaele De Vita had capped off a bright start to the contest for Parkinson's side by firing in his first goal for the club on thirteen minutes.
Parkinson added: "It was great for Raf - he always gets chances.
"He had one today and he had one against Preston on Tuesday.
"I am so pleased for him to get his goal today because he is terrific lad. He has worked his socks off since he has come here."
This Saturday's Wolves encounter saw the much-anticipated return of Nahki Wells following his month away due to a recent ankle problem.
Wells' half-time introduction from the substitutes' bench came about after De Vita was withdrawn due to tightness in his hamstrings.
City's popular Bermudian wasted no time in reintroducing himself to League 1 football once again, with the forward testing the visiting defence on more than one occasion.
Parkinson continued: "To ask Raf to go again (after the Preston game on Tuesday) after he hasn't played in a while was always going to be tough. Unfortunately his hamstrings did tighten up.
"Nahki looked a threat today and his partnership back with James (Hanson) again looked like it could get us a goal.
"That is why I left our shape (4-4-2) as long as I could. I knew if I disrupted it too early, we could get hurt on the break."
In a second period that saw City take the game to their visitors, Kyel Reid was controversially booked for diving after the winger fell in the box as Wolves 'keeper Carl Ikeme dived out at his feet.
After seeing the penalty shout turned down and Reid cautioned, Parkinson admitted he is starting to get a little concerned that City have yet to be awarded a spot-kick at any point this season despite several convincing appeals.
Parkinson added: "I have had the benefit of seeing the incident again and I feel it is a penalty.
"Leading up to the game, I did my homework on Wolves' penalties this season to let Jon (McLaughlin) know where their takers have been putting them. Kenny (Jackett, Wolves manager) won't have had to do that for us because we haven't had one.
"Today is another example of where the decision hasn't gone for us. I don't agree with the decision the referee came up with. I thought at the time Reidy may have gone slightly easily, but there is definite contact there and the ball was right at his feet for him to slide it across goal. There was no need for him to go down if he hadn't been touched.
"It was a very harsh decision not to get.
"Surely though, we are going to have to get a penalty decision go our way. Not to have one by this stage of the season, with all the attacking play we have created, all the attacking players we have and the amount of time we spend in the opposition's penalty area, is very frustrating.
"I could name a long list of incidents we've had this season where a penalty could have been given for us, so I am getting frustrated by it all."