Returning to the second tier after a tumultuous two-year stay in the Premier League, Nedum Onuoha and Andrew Johnson netted in quick succession as Rangers recovered from Atdhe Nuhiu’s early strike.
As good as QPR were in the 2-1 win, Jones felt his side were robbed of at least a point at Loftus Road.
Michail Antonio saw a penalty appeal waved away in the first half when Wednesday were ahead, before Jacques Maghoma was given a yellow card by referee Scott Mathieson for diving when caught by just-booked Joey Barton.
Jones believes the referee had a “shocker” and risked the wrath of the Football Association as he ranted for 17 minutes about the officials’ poor display.
“I don’t even think it is unlucky, I think it is an embarrassment for the official to miss the two clear-cut penalties,” the Owls boss said.
“You need big calls at places like this in front of a big crowd. You need a big referee to make a big call and he didn’t do it.
“We just lost our concentration and they capitalised on that. To add insult to it, he then goes and books him and says it is a dive.
“He will go home tonight, put his feet up and get another game - and I don’t think it is right.
“I don’t know where you will put him. I don’t know what league you would put him in because if you can’t pick that out there, he won’t pick it out anywhere.
“Something has to be said - they can’t keep making those mistakes. They are two big calls.
“It was a good game and I feel for my players. They worked hard, were unlucky. Michail should have scored, we hit the post. I think we deserved to come away with something from the game.”