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, 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."
QPR assistant Kevin Bond appeared in place of manager Harry Redknapp in the post-match press conference and understood Jones' frustration.
"I haven't actually seen either of them," he said. "I am led to believe the second one was a penalty.
"All I would say in defence of the officials and all officials is that I don't ever think they mean to give a wrong decision.
"He did it in best faith and that's all you can ask. The guys have an impossible job and I think they need help.
"Like you get in others sports like tennis and rugby, I think they need TV replays or something for the big decisions.
"Whether they give clubs a couple of calls each half, I don't know. It has always happened and will always happen."
The officials' decisions overshadowed what was an impressive QPR performance and one which saw Barton make his first appearance for the club in 447 days.
Barton spent last term on loan at Marseille and was adamant in May he would not play in the Championship this season.
Yet today he started for Rangers and impressed in midfield, although he may yet still leave before the transfer window shuts.
"I don't know what the future holds for Joey Barton," Bond said.
"Since he has been with us, he has trained well, conducted himself well and Harry was going to pick the best side to win the game today.
"I am not sure Joey Barton knows what the future holds for him but I thought he did a really good job for the team today."