Shaun Miller gave the hosts a fourth-minute lead and Scunthorpe never recovered from that early setback. After Scunthorpe's Damien Mozika hit the bar, Dave Kitson headed a second goal and Nick Blackman's 84th-minute penalty completed the scoring after Tom Newey fouled Ryan Flynn inside the area.
"I thought the performance was outstanding at times. Some of the football was terrific and the goals that we scored were top drawer. We've had a big crowd and they've seen some good football and some good goals and it always whets the appetite for the next one. I hope we can repeat that on Saturday," Wilson said.
"We had to re-adjust following injuries to Shaun Miller and Neill Collins but I thought we settled down quickly. Shaun Miller has got as problem with his knee but we're not too sure about the extent of it. We're not too sure about him yet and it will be at least 48 hours before it can be assessed.
"There's more clarity with Neill Collins' injury. We think he's fractured his cheekbone so he's in hospital. It was quite depressed so it looks like he'll be out for a few weeks. Unfortunately, this happens in football at times and you have to accept it and move on."
Scunthorpe manager Brian Laws saw his side lose for the fourth time in five league games, leaving them mired in relegation trouble.
The former Sheffield Wednesday boss said: "I'm disappointed but I don't think we can argue about the result because Sheffield United punished us for the mistakes we made. Particularly the first goal, which was our own undoing.
"I have to say that in the first-half, I thought we were the better side. With the opportunities that we had, we should have come in at least on level terms. Damien (Mozika) missed a clear sitter from six yards.
"I thought we were trying so hard to get a goal back. It showed the mentality of the players that it wasn't going to affect them. We should have got a reward for out first-half performance but we didn't. Once that second goal went in we had to change and we left ourselves open after trying to change the game.
"It was quite an aerial battle against a very big side in Sheffield United. We took some knocks and bruises but we certainly didn't crumble because of it."