Parkinson launched a strong criticism of VAR after his side’s dramatic fifth-round defeat to Chelsea at the Racecourse Ground.
Wrexham pushed the Premier League visitors all the way before eventually losing 4-2 after extra time, but Parkinson believes the match will ultimately be remembered for the controversial interventions of the video assistant referee rather than the quality of the winners.
It was the first time the north Wales club had experienced VAR in action, with the technology not used in the EFL Championship or in the earlier rounds of the FA Cup.
Parkinson admitted he felt the system had a major influence on the outcome and argued: "It's such a shame that our first taste of VAR has gone this way because it will be the talking point.”
Wrexham had twice taken the lead in front of a packed crowd and appeared on course for one of the competition’s great upsets before the match turned dramatically in the closing stages.
The most controversial moment arrived deep into stoppage time when midfielder George Dobson was initially shown a yellow card for a challenge on Alejandro Garnacho.
After being called to the pitchside monitor, referee Peter Bankes upgraded the punishment to a red card following a VAR review.
Parkinson believed the intervention was unnecessary.
"I thought VAR was meant to be for clear and obvious decisions. Dobbo's gone in with force. The referee is in a good position to see it. He has scraped his shin.
"It's caught him low down. I thought he could've easily kept that as a yellow. In my opinion, I don't think the VAR should've intervened.
"It was a tight call and if that's the case you should leave it with the onfield decision."
The dismissal left Wrexham with ten men just as the game was heading into extra time and proved a turning point in the tie.
Parkinson later expanded on his frustration, arguing that the referee had been perfectly positioned to judge the challenge without technological assistance.
"The first taste of VAR here at the Racecourse, and I know the rule is it's got to be a clear and obvious mistake for the on-pitch decision to be changed," he said.
"I think the ref's got to back his judgment of the real time incident and moment.
"Of course, when you get called over to a screen, which I don't he you should have done, and you analyse it and scrutinise it, they'll say that he's caught him on the shin, but he's scraped his shin.
"But he's in a great position to see the initial incident, and I think it's very harsh and should have kept with the on-pitch decision."
Despite the setback, Wrexham continued to fight and thought they had forced a dramatic equaliser during extra time when Lewis Brunt turned home following a flick-on from Kieffer Moore after Lewis O’Brien’s delivery.
However, celebrations were cut short after another VAR check ruled Brunt marginally offside, denying Wrexham a goal that would have made it 3-3.
Parkinson acknowledged the decision itself was technically correct but still felt the margins were painfully tight.
"The offside', it's marginal. Is Kieffer's header going in anyway? But Brunty is always going to finish that off in that situation.
"It's marginal so we can't complain if that was offside but I think the red card and now to lose a player for three games is a tough decision.”
Chelsea eventually capitalised on their numerical advantage. Garnacho and João Pedro both found the net in extra time to secure the visitors’ progress into the quarter-finals after a performance that at times looked far from comfortable.
For much of the night, it had been Wrexham who looked the more dangerous side.
Sam Smith gave the hosts the lead in the 18th minute when he latched onto Callum Doyle’s long pass over the top and finished calmly beyond goalkeeper Robert Sanchez.
Parkinson was full of praise for the striker’s performance.
"Sam carried a real threat," said the Reds' boss.
"It's a great run and a good finish. He had another chance when he checked back in but I thought he played well.
"It was a good test for us and. I said to Sam, playing against good centre-halves, Rory Delap a £60 million pound player playing for them, let's hope people are talking about you after the game and they so nearly were.
"Those moments could and maybe should have been part of a winning performance."
Chelsea equalised before the break, but Wrexham regained the lead early in the second half when Doyle struck. That advantage lasted only four minutes before the visitors levelled again to force the game into extra time.
Parkinson admitted the second equaliser came after a costly error but was encouraged by how his team responded throughout the contest.
"A slip on the edge of the box and we got punished for it. You'd rather that didn't happen, but it did," he added.
"You get setbacks within games of football, and it's how you respond, and I was pleased that when those moments happened, the sending off after the goal, we kept going and kept believing there was something in the game for us."
