Junior Hoilett gave QPR a second-minute lead when he raced the length of the pitch from a Toffees corner and beat Tim Howard.
However, the visitors drew level after Sylvain Distin’s header crept across the line in the 33rd minute, albeit aided by large deflection of Júlio César.
Steven Pienaar was sent off for a second bookable offence in the 60th minute, but Hughes’ men were unable to find a way past a stubborn Everton defence.
“I think that’s the frustration we are all feeling. We showed today our football is good and we try to play in the right manner,” said Hughes.
“We try and play with width and encourage our technical players to take people on, and we’ve done that since the beginning of the season and had good performances.
“But we haven’t been able to take that final step of getting three points on the board which is what we’re here to do. So that is why we’re really frustrated.
“This was an opportunity. Obviously with a man advantage against a team in the Premier League, you hope you can go on and take the game away from them.
“Like I said, Everton are an organised and very accomplished team. They’re strong and powerful, and they dug in.”