Derry was sent off for denying Ashley Young a clear goalscoring opportunity, but TV replays showed the decision was debatable and the United winger had been offside anyway.
The midfielder is set to miss Wednesday's encounter with Swansea at Loftus Road, but Hughes will challenge the dismissal.
"Yes. We will appeal the red card," said Hughes.
"We need all hands on deck on Wednesday, plus Shaun has had a rest. He only played for 15 minutes."
The QPR boss said that the standard of officiating is a major cause for concern.
"You do discuss it before every game," added Hughes. "You worry more about decisions going against you and it shouldn't be like that.
"You should have confidence that the referee will get the key decisions right. Just lately a lot of managers have lost faith in them.
"It is a difficult job. You have to be strong and really clear. You have to be 100 per cent right to give the decisions. At the moment people are guessing and hoping that they get it correct. That was the case today."
QPR chief executive Phil Beard labelled Young a diver and likened him to British Olympic diver Tom Daley in a Twitter post that was re-tweeted by QPR majority shareholder Tony Fernandes.
"Difficult to take after watching numerous replays but Ashley Young could partner Tom Daley at the Olympics #QPR," he wrote.
QPR director Ruben Emir Gnanalingam was also aggrieved, pointing to the fact Young also appeared to be offside in the lead-up to the incident, adding: "It was offside and a dive by Young! Alex Ferguson's luck with calls continues. Just wish there was video technology!"
Fernandes replied to that tweet, saying: "Awful. Spoilt another game."
He then added: "Thank you to all the manchester united (sic) fans for their honesty. Have received 150 tweets saying he was offside and was never a penalty."
Meanwhile United manager Alex Ferguson, who has now gone 30 successive matches without a loss against one of his former players turned coach, had huge sympathy for Hughes.
"Ashley was a yard offside and I understand why Mark is angry. There have been a lot of decisions like that in the last few weeks," he said.
"I was more confident before the man was sent off because the speed of our play and the movement was very good. After that we were just in a comfort zone.
"The only thing I can say is we have won the game. There are only six games left and we're now a goal better off than City."