City were piling on the pressure in their search for an equaliser when goalkeeper Carl Ikeme dived at Kyel Reid’s feet as the winger burst into the area in the 66th minute.
Reid went flying under the challenge, but instead of awarding a penalty, the referee booked Reid for diving.
Parkinson said: “I was so frustrated we didn’t get a penalty. I have seen it on DVD and it was a clear penalty – the goalkeeper has taken him out.
“Why would Kyel Reid go down when he could have slid the ball across the box? It was a terrible decision.”
Bradford made a great start, going in front after 14 minutes with a first goal for the club from Italian-born midfield player Raffaele De Vita. His first shot was blocked by defender Danny Batth, but De Vita fired home the rebound.
However, Wolves hit back with two goals in four minutes that ultimately gave them their fifth away win in a row and lifted them into second place.
The equaliser after 28 minutes was the result of a mistake by Jon McLaughlin, the goalkeeper allowing James Henry’s 20-yard shot to creep under his body.
Before Bradford could recover, Wolves took the lead after 32 minutes. Henry’s corner was only partially cleared and when he returned the ball into the goalmouth, defender Richard Stearman reacted quickly to head the ball into the net.
At half-time, Parkinson sent on leading scorer Nahki Wells, who had missed the previous four matches with an ankle injury, for the injured De Vita and the Bermudan international spearheaded Bradford’s spirited quest for an equaliser along with captain Gary Jones.
Wells saw a left-foot effort deflected for a corner and, with three minutes to go, he had two point-blank shots blocked, one of them superbly by Ikeme.
Despite the onslaught, the visitors held firm as City slipped to their third defeat in four matches.
Parkinson said: “We started great, but their first goal was really poor – Jon McLaughlin will be disappointed with that – and they got another one quickly. We took our foot off the pedal slightly and got punished for it, but in the second half we were excellent.”
Bradford City: McLaughlin, Darby, McArdle, Bates (Folan 85), Meredith, De Vita (Wells 46), Jones, Doyle, Reid, Hanson, Thompson (Yeates 70). Unused substitutes: Ripley, Kennedy, Taylor, McHugh.
Wolverhampton Wanders: Ikeme, Stearman (Ebanks-Landell 59), Batth, Henry, Davis, Griffiths (Sigurdarson 79), Sako, McDonald, Evans (Doyle 24), Ricketts, Golbourne. Unused substitutes: McCarey, Edwards, Forde, O’Hara.
Referee: G Salisbury (Lancashire).
Man of the match: Gary Jones.