Mikel Arteta prodded the ball home six minutes from time to leave QPR bottom of the table, but Hughes was adamant the Spaniard was offside and was not accepting the referee's explanation for the decision.
"I can't remember any clear-cut chances they had while we had 11 players on the pitch, but with the sending off, that changed the make-up of the game," Hughes told Sky Sports.
"We conceded a goal during that period and when the referee sees it again he will understand he has made a huge mistake as the lad is clearly offside on two occasions leading up to the goal.
"When you're in the situation we're in, with not many points on the board and down to 10 men, you need officials to get the key decisions to help us along the way and we didn't get it from them.
"I've been in to see the referee and he has conjured up some story about Ryan Nelsen that, because he left the field of play he played everybody onside, but I've no idea what he's g oing on about because Ryan Nelsen didn't at any stage leave the field of play.
"He'll have to explain that one to me because that has hurt us."
Regarding Mbia's red card for kicking out at Thomas Vermaelen, QPR boss Hughes was disappointed by the Arsenal captain's reaction.
He added: "That's a frustration because the linesman has actually given a free-kick our way.
"Stephane was on the floor and he has swung the leg, there is very minimal contact and Vermaelen is going to make the most of that situation. He dives and rolls around, and makes sure the referee makes a decision.
"There is contact and it's a wild challenge. It's a sending off that has really hurt us at a point in time when we're making positive substitutions as there was a real opportunity to get three points."
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