But Salisbury was unimpressed and opted to book for 'diving', which left Parkinson cursing his luck.
Parkinson said: "I was frustrated we didn't get a penalty.
"I have just seen it on DVD and it is clear it was a penalty. The keeper has taken him out.
"Why would Kyel Reid have gone down when he could have slid the ball across the box? It was a terrible decision.
"We started off great, but their first goal was a really poor one from our point of view and then they got another very quickly.
"I thought we took our foot off the pedal slightly and got punished heavily for it.
"It should have been a routine save from Jon McLaughlin, but he has pulled off some fantastic saves for us this season.
"He will be disappointed with that, but we did everything we could to rectify that mistake and we were excellent in the second half.
"I don't think we could have done much more against a team with millions of pounds worth of talent at their disposal."
Bradford began well and were rewarded in the 14th minute when Italian-born midfielder Raffaele De Vita put them in front with his first goal for the club since joining them from Swindon in the close season.
Wolves then shook Bradford with two goals in four minutes.
Millwall loanee James Henry equalised after 28 minutes when a mix-up between skipper Gary Jones and James Meredith left him with a clear shot on goal and his 20-yard shot appeared to go under keeper Jon McLaughlin's body.
The visitors went ahead after 32 minutes when Henry's left-wing corner was only partially cleared and when he returned the ball into the goalmouth defender Richard Stearman reacted quickly to head the ball home.
Parkinson brought on leading goalscorer Nahki Wells, who has missed the last four games with an ankle injury, and he and Reid posed the greatest threat to the Wolves defence as Bradford battled for an equaliser.
Wells and Reid both had shots blocked in the 76th minute and keeper Carl Ikeme made a superb effort to deny the home side three minutes from the end.