Cabango missed the ball in the 77th minute challenge and caught O’Hare, who was making his debut after a £6.5m deadline day move from Sheffield United.
Swansea boss Vitor Matos did not want to get involved in the debate after the game, saying: “I never comment on ref decisions, in one way or the other. If he [Parkinson] says that, good for him.”
O’Hare claimed Cabango should have been sent off, saying the 16-cap centre-back told him he “didn’t touch” the midfielder.
Parkinson added: “Cabango grabbed Kieffer around the neck on the halfway line before that. A yellow card and then the tackle.
“The same referee has sent Callum Doyle off against Oxford last season for a tackle, which maybe he was slightly out of control.
“But I’m very interested to ask the referee when he compares both those incidents. How he differentiates between the two, because every year, managers have to sit and listen to the referees about what they deem to be red cards, and when you’re out of control, like Ben Cabango was and endangering a player. That is a straight red card.”
Wrexham still had chances to win the game, but Parkinson said he was pleased with the efforts of his side on the back of a first win of the season, Wednesday’s midweek triumph at Millwall.
“I thought we’d got better as the game went on and you know, we looked at an experienced team with a lot of football intelligence to like,” said Parkinson, whose side welcome Burnley on Tuesday before a trip to West Ham United on Friday.
“You’ve got to stay in games with the offensive kind of bravery in situations, but also concentration levels and I thought in the last two games we’ve done that really well and we can take a lot of credit for that.”