Billy Sharp’s early opener against his former club was cancelled out by Kalvin Phillips’ volley before half-time, but substitute David Brooks fired a deserved winner to send the Blades top of the second tier for the first time in 12 years.
“We’re delighted with the result, but I’ve got to say - and I’m not trying to deflect anything - but if you’ve seen us play this season, especially in possession, we were quite loose today,” Wilder said.
“That frustrated me a little bit because we’re usually better in possession and keep the ball better and we turned the ball over far too much and allowed them into the game too much.
“I’m not disrespecting the opposition, but from our point of view we’ll keep looking at what we’re about and how we can improve.
“I thought we got caught up in the occasion a little bit, especially in the second half when they got a head of steam up.”
Leeds goalkeeper Andy Lonergan made brilliant first-half saves to twice deny Sharp as the Blades tore into their Yorkshire rivals from kick-off.
Samuel Saiz crashed a shot against a post in the second period as Leeds forced their way back into the game and Ezgjan Alioski wasted a headed chance.
Wilder saluted match-winner Brooks, whose first senior goal six minutes after stepping off the bench secured the Blades their ninth win in 11 league matches.
“I’m not going to hide away from the fact that he’s a decent player,” Wilder added.
“He was due a goal. He’s had four or five good opportunities that you would expect (him to score).
“What you see from him Monday to Friday - usually he finishes them, so it will be good for his confidence.”
The Blades last sat top of the second tier in November 2005 and Wilder added: “Yes we’ve got a target on our back, we understand that.
“We have to handle the bigger games. That’s not being disrespectful to the other games, but I don’t think it comes much bigger at this moment than third versus fourth. A Yorkshire derby, two teams having a right go at it in front of 35,000.”
Leeds head coach Thomas Christiansen could not hide his disappointment after his side slipped to a fifth defeat in seven league games.
“I cannot be happy, of course,” he said. “The result is what we all want - the three points and we weren’t able to take them.
“It wasn’t a good performance. We have to be honest with ourselves. The way we acted in the first half was not good enough.”
Christiansen confirmed skipper Liam Cooper, forced off in the second half, sustained a dead leg.