Newcastle were already leading at Bramall Lane courtesy of Allan Saint-Maximin's early header, before some intelligent play from Jonjo Shelvey saw the visitors double their lead midway through the second half.
Paul Dummett's long ball forward was flicked on by Andy Carroll and Shelvey found himself clean through on goal after making a run from deep.
The linesman put up his flag and the Blades defenders totally stopped playing, believing the Newcastle midfielder to be offside, while goalkeeper Dean Henderson made no attempt to save the ball as Shelvey fired into the back of the net, knowing the goal would be checked.
It was a very tight decision but Carroll was inches onside and the goal stood to seal a 2-0 victory for the Magpies.
Asked about the incident post-match, a clearly frustrated Wilder said: "It sucked the life out of my players, but more importantly it sucked the life out of 30,000 Sheffield United fans.
"It (VAR) is becoming too difficult for everyone. I don't think anyone knows where they are with it. The game has changed, it's a new game. What we are having to deal with, we're having to learn on the job.
"Every interview that I do post-game is VAR-based, the majority of the time it is. I'm drained with it, if I'm honest. We are learning a different game and I am a bit saddened by it."
The defeat to the Magpies means the Blades missed out on the opportunity to move into sixth place in the Premier League, while Newcastle move up to 11th and are now level on points with Wilder's side.
United will be looking to get back to winning ways on Sunday when they make the trip to struggling Norwich City.