It was former Blades star Kyle Walker who scored the winner, smashing home a shot from long-range at the ground where he began his professional career.
United created decent chances of their own, but couldn't get back into the game as their wait for a first victory of the season continued.
And Wilder said afterwards: "We want points on the board, not plaudits. I'm saying the same things after games, we've been in every one but that's not enough to start picking up points.
"From a motivational point of view, I shouldn't have to hit them with that stick, and I don't. We have to be better with the ball.
"If people think we can open up to City, they haven't got a clue about football. Their world-class players will pick you off and it can be three, four or five.
"We had to stay compact, they're one of the best teams at pressing you so you can't think 'we'll roll it out and play through them'. When it was our time to play, we had to show more quality than we did.
"We kept turning it over and the obvious quality they have showed."
City manager Pep Guardiola said: "We played really well. We struggled to score goals for the chances we created.
"But they had one clear chance, no more than that, and I'm incredibly satisfied, it's so important."