The Blades struggled to break down lowly Reading, but a late header from Billy Sharp and a Sam Baldock own goal eventually secured the points.
“It was a great win for us, but I wasn’t too pleased with the first-half performance,” Wilder said. “We kept them at arm’s length, but we were not anywhere near where our usual standards are.
“So I made a little change at half-time and had a few harsh words with the players.
“We were away from home and we had no divine right just to turn up. I just wasn’t happy with our general overall display. But I thought that we came roaring back in the second half and were much better.
“We dictated the game and I think it was the right result in the end.
“We had a couple of ‘goals’ disallowed, which were the correct decisions, but we kept knocking on the door.
“I always thought that there was a win there for us and if there wasn’t it wasn’t for the want of trying. We drove the game forward and I’ve got nothing but praise for my players.”
United had two ‘goals’ chalked off for offside in a dour first period in which neither team impressed.
Reading then proved stubborn opposition after the interval and United were indebted to top scorer Sharp, who came on as a second-half substitute to nod in his 12th goal of the season in the 83rd minute.
Three minutes later Reading striker Baldock headed into his own net from a John Fleck corner.
The Royals sacked manager Paul Clement on Thursday, with Scott Marshall, the club’s Under-23s boss, installed as first-team caretaker boss.
Marshall said: “I’m disappointed with the two late goals. It’s a sore one to take.
“It was also disappointing to concede in the manner that we did.
“We had opportunities to pass and play and link up a little bit, but we’d liked to have worked their goalkeeper a little bit more,” he added.
Reading: Jaakkola, Yiadom, Tiago Ilori, Blackett, Gunter, Rinomhota, Bacuna, Sims (Barrow 64), Loader, McCleary (Aluko 85), McNulty (Baldock 64). Unused substitutes: Mannone, Swift, Kelly, McIntyre.
Sheffield United: Henderson, Basham, Egan, O’Connell, Baldock, Lundstram (Duffy 46), Norwood, Fleck, Stevens, Washington (Sharp 60), McGoldrick. Unused substitutes: Coutts, Stearman, Johnson, Moore, Cranie.
Referee: J Linington (Isle of Wight).