The striker was rightly booked in the first half of the goalless first leg at Tannadice following a penalty box dive - but footage showed he was clearly caught on the knee by Scott McMann in the penalty area before being sent off in the 77th minute.
McKinnon confirmed he would "absolutely" appeal against Murray's second yellow card, meaning the striker will play in the second leg at the SuperSeal stadium on Sunday.
Referee Steven McLean acted on the advice of assistant Graham Chambers which left the former Terrors midfielder frustrated.
He said: "At the time we thought it was a penalty to begin with.
"The referee obviously gives the decision against us and books Simon for simulation which is his second booking and sends him off.
"We regrouped, went to a 4-4-1 to see the game out but it was disappointing to see the incident back, television points out it it was a stonewall penalty so it was very disappointing for the referee.
"It would be an injustice if Simon Murray couldn't play in the game on Sunday, through no fault of his own.
"We will certainly appeal and deal with that tomorrow morning
He is a massive part of the team
It is absolutely vital he is back in the team on Sunday."
McKinnon also suggested the future looked bleak for Wato Kuate.
The midfielder clashed with team-mate Mark Durnan on the park and sarcastically clapped the United fans as he made straight for the tunnel when replaced shortly afterwards
Asked if Kuate had played his last game for the club, McKinnon said: "It might be, we will see.
"I will look at that back and take stock tomorrow
There is no point in me getting emotionally involved
"I didn't speak to him, I spoke to the rest of the players with regards to their efforts especially when they went down to 10 men."
Hamilton boss Martin Canning did not have a view of the second sending off but was reluctant to admit the tie had swung towards Accies.
He said: "It will be a difficult game because there are two teams who are evenly matched.
"I don't think it matters if it's at our place or at their place
It's still 0-0.
"We would have taken a draw before the game but we came here to win it.
"We will approach Sunday in the same way as we did tonight.
"We had good chances in the first half but we didn't take them and that has been the story of our season really."
Source : PA