The visitors were reduced to ten men when Steven Pienaar received his marching orders for two soft fouls in the space of 10 second-half minutes, before Moss chose not to award QPR a "stonewall" penalty following Seamus Coleman's clumsy trip of Junior Hoilett.
Hoilett had given bottom-of-the-table QPR the lead after just four minutes before Julio Cesar contrived to turn Sylvain Distin's header over his own goalline after it rebounded back off the post, leaving the two sides level at the break. By the hour mark, David Moyes' side were a man light as Pienaar saw red for a foul on Jose Bosingwa.
The Everton manager told reporters of the incident: "It was very, very harsh to give somebody a red card for that, incredible.
"We actually watched a clip last week on Jelavic, very similar – we didn't get a penalty for it against Wigan two weeks ago – this one, I don't know if he even clipped the boy.
"I think he hit Steven's rather than Steven clipping him so I think it was the wrong decision, definitely."
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The decision not to award a spot-kick incensed Hughes, who complained in the post-match press conference: "In the end, we should have had a stonewall penalty anyway, the referee was only four metres away so why he hasn't given it, I have no idea.
"But in fairness, he frustrated both teams and both sets of supporters today... Not one of his better games."
The Loftus Road outfit remain anchored to the bottom of the Premier League after failing to claim a maiden win in eight attempts, but Hughes remained buoyant following a performance full of positives.
"We've gone up against a team that has started the season like a house on fire and more than matched them and on another day should have beaten them," he added, before bemoaning the lapse in concentration that cost the team three points.
"We're pleased with the level of performance in the first half, albeit we've let ourselves down on a set-play where we need to do a lot better than we did and take responsibility to stay with your man.
"You shouldn't allow a big powerful centre-half have a free header from six yards. That shouldn't happen."