But substitute David Brooks came on with 15 minutes to go and scored the Blades' victor six minutes later.
"I thought we picked it up a little bit second half". "Whatever happens, I'm sure we can do that".
"Thomas [Christiansen] will be disappointed with the outcome of the game and I think he will have gone in at half time as the happier manager from the point of view we went in level at half time, when they maybe looked like they should have scored a couple of goals".
Leeds did improve their performance from the start of the second half and could have gone ahead had a shot from Samu Saiz not hit the post.
Leeds goalkeeper Andy Lonergan made brilliant first-half saves to twice deny Sharp as the Blades tore into their Yorkshire rivals from kick-off.
Wilder, who will watch Wolves attempt to regain top spot at Queens Park Rangers today, said: "We looked for a little bit of magic from somebody to decide a tight game and the young boy got us into the lead".
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How desperate they must be that their Blades-supporting boss, who has a United tattoo, stays put. He's had four or five good opportunities that you would expect (him to score).
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".
"Always when I lose I have a face like I could kill somebody but I will try to sleep and tomorrow I will face the team and we will fight back again". 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.
Though Wilder later said: "This is Yorkshire on a Friday night between two committed teams in front of 35,000 people".
"I can not be happy, of course", he said. Three points is what we want - tonight we weren't able to make it. We have to be honest with ourselves. He then calmly placed the ball back across goal with a first-time shot to find the bottom right corner in the 81st minute.
Pontuss Jansson replaced injured Leeds skipper Liam Cooper in the 56th minute, but and Christiansen admits it was just a dead leg.
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