Wilder criticised two "major decisions" from officials as Ezri Konsa's second-half header gave Aston Villa victory over the Blades, who played for 78 minutes with 10 men.
Wilder questioned referee Graham Scott's decisions to send off John Egan early in the game and not show a red a card to Villa's Targett for conceding a penalty, which John Lundstram saw saved by Villa debutant Emiliano Martinez with the score at 0-0.
"Why didn't the referee go over to the monitor? I wouldn't come out here and mug myself off - if I thought it was a clear sending-off I'd say so," Wilder said.
"Why didn't he go to the monitor? Why didn't Stockley Park [where the VAR officials are based] say 'it's a bit of tussle and look at it yourself'?
He later added: "The penalty - Egan gets sent off 35 yards from goal, Matt Targett makes no effort to win the ball.
"The double jeopardy is only when the opposition player makes a challenge for the ball, the ball is four yards away, so [he can't reach it] unless he's got spider legs he can wrap around - and he hasn't because I've watched it."
Villa boss Dean Smith stated, "A very good start, to get three points and a clean sheet you can't ask for more. I thought we stared the game the better and the game changes with the sending-off.
"We've worked on Tyrone Mings getting across the near post, flicking it on and Ezri Konsa arriving. It's difficult when they go in with two banks of four. We probably should have scored more. Since lockdown, defensively I think we've been more aggressive."