United slipped to sixth in the table, five points behind second-placed Leeds, after being narrowly beaten by Marcelo Bielsa's side.
But a defiant Wilder, who backed goalkeeper Dean Henderson to bounce back from the mistake which gifted Pablo Hernandez the only goal of the game, said: "We should not be anywhere near. Seriously, we should not be anywhere near.Â
"We're getting the maximum amount of the players, the absolute maximum. And they are given the maximum for this football club. But we should not be anywhere near and we shouldn't have been anywhere near it last year either."
United, who also challenged for the play-offs last term after winning promotion the season before, are expected to target a centre-forward and attacking midfielder during next month's transfer window. With fellow contenders Nottingham Forest, West Bromwich Albion and Middlesbrough all expected to spend heavily in an effort to bolster their squads, Wilder is hoping to receive a significantÂ portion of the near Â£12m fee AFC Bournemouth paid for David Brooks to reinvest after Christmas.
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Expressing frustration with some of the narrative surrounding United's recent performances, he said: "It so winds me up when people say we fell away after Christmas (last season). We shouldn't be anywhere near it now to fall away.Â
"But that's how it is. That's for another day.Â
"I'll back my team and we'll give it a real good go. Sheffield United want to see their supporters walk in the front door and go out of the front door. I thought we did that today. We should not be anywhere near but we are and so we'll have to recover."
United created numerous opportunities before Henderson's misplaced pass set in motion the chain of events which ended with Hernandez scoring the only goal of Saturday's match.
"John (Egan) has played a tight back pass but he (Henderson) has got to get on with it," Wilder continued. "It's not for me to rub his head is it. If he wants to play at the top, he's going to have to make mistakes. But his attitude and performance afterwards told you he'll be okay."
"I don't think it was us on the back foot for the majority of the game," Wilder added. "I don't think it was them on the back foot for the majority of the game.Â
"It was good that it was well contested. That's what you want. There were contrasting shapes and they had a decent period midway through the second half but there were a lot of periods when we were really good.
"We probably should have scored before half time but we didn't. Nobody, though, connected with this football club, can be disappointed with what the boys are doing."
Bielsa, the former Argentina and Chile manager, was full of praise for United's approach afterwards; citing their over-lapping centre-halves and revolving midfield as a "project" worthy of "study".
"We go our own way," Wilder said. "I'm not sat here saying we are reinventing the wheel or anything. We just play in a way that suits us. We tweak it and try to cause the opposition problems.Â "Good teams and good staff will try and find a way to win the game and good players will try to implement those methods and instructions. I think my team plays with a freedom and is competitive."