The Owls boss was convinced home striker Marvin Elliott fouled his goalkeeper Chris Kirkland as he came off his line to intercept a cross in the build-up to Sam Baldock's goal.
However, referee Darren Deadman allowed the goal to stand and Jones was unable to contain his anger.
"It was a forearm smash by Elliott. Anywhere else on the pitch it would have been a free kick," said Jones. "We had taken everything City could throw at us and all you ask is a fair deal from the match officials.
"We have had trouble with this referee before. If he had done his job we would have been going home with three points, but I get tired of saying that sort of thing.
"We scored a great goal and Chris Kirkland has hardly had a shot to save. I feel so frustrated for my players.
"The relegation battle is going down to the wire. But we already knew that before this game."
Jermaine Johnson had fired the away side into the lead in the 36th minute.
Despite creating a number of good chances throughout the match, it looked like City were heading for their 22nd defeat of the season until Baldock's 92nd-minute goal.
The Robins remain bottom of the table, seven points from safety, while Wednesday are only out of the relegation zone on goal difference.