Referee Mick Russell made a glaring error midway through the first half when he failed to send off Owls midfielder Helan for a second yellow-card offence.
Helan, on loan from Manchester City, was emerging as the game's outstanding player when he was booked by Russell for a 26th-minute foul on Huddersfield winger Adam Hammill.
But the Hertfordshire official did not realise he had already booked the Frenchman for diving in the penalty area in the ninth minute and despite animated reminders from Huddersfield players and the home bench, Russell restarted play with Helan still on the pitch amid chants of 'you don't know what you're doing'.
Jones was adamant Helan should not have been booked early on and that his side should instead have been awarded a penalty.
Jones, whose job is looking a bit more secure now than it was at the end of last month, said: "I don't know about a first booking, it was a penalty. That's the controversy.
"Helan has been clipped and he's not the type of lad to do that (dive). I think we should have won the game, that's what I'm perplexed about.
"We should have had a penalty and we had the chance towards the end with (Mamady) Sidibe's header."