The visitors were already leading as Michail Antonio had capitalised on a lapse from keeper Jonathan Bond after he had been played into trouble by Marco Cassetti when Bond made a fine save to push a powerfully-struck Miguel Llera free-kick up into the air.
Lewis Buxton's follow-up header appeared to cross the line and then Nyron Nosworthy seemed to handle. Wednesday had other chances to extend their lead in the first half but Gianfranco Zola made a double change at the break and one of the substitutes, Fernando Forestieri, turned the game around with a second-half brace.
Asked about his side's fine first-half display, Jones said: "What can I say, we should be 2-0 up. I don't know how the referee and the linesman miss it. He either gives hand ball or he gives the ball across the line, he can't miss both and he did. And that changes the whole complexion.
"Instead of going in 2-0 up, we go in 1-0 up. I don't know what you do because it's not acceptable for both teams. Some of the things he was doing...me and Franco [Gianfranco Zola] on the line, it's not a laughing matter, but I don't know what to say because I thought we were absolutely magnificent.
"Everyone's appealing and yet the two guys who shouldn't miss it do. It can't keep going on. Anyone who gets paid and it's their livelihood, he should not be officiating at this moment in time.
"He should be dropped down to wherever they drop them, see the referee psychologist or whoever else they see and have a good look at that for 90 minutes because that is probably one of the poorest performances I've seen for a long time."
Watford are now unbeaten in seven and Zola said: "We know that it is getting tight for everyone, all the games are really difficult and so you need to win games differently. The quality [substitutes] that we put in to the second half has made a difference and it covered some of the difficulties that we had during the game, especially in the first half.
"They created a lot of problems and fortunately the two players that came on in the second half [Nathaniel Chalobah and Forestieri], they gave the excellent quality that we needed to edge to the win.
"They've really made a big difference. That's what you need when sometimes things don't work well, you need to be able to change things when it's needed and Fernando and Nathaniel did exactly that."