Leeds-born Oli McBurnie’s 11th goal of the season extended Swansea City’s unbeaten run to five matches.
“I thought we were outstanding in the first half in the way we controlled the game against a really talented group of players,” said Wilder.
“But we should have put the game to bed. We should have been two up at half-time and I shouldn’t have been making changes after half-time to get back into the game. I should have been making changes to see out the game.
“In the first 10 minutes of the second half we got a little bit sloppy. They changed their shape, which gave us a little bit of problem, but we allowed them a foothold into the game. They had one bit of quality, but we did that half a dozen times and couldn’t find the finish.
“Then, when we were chasing the game, we were disappointed with the final ball.”
As Wilder noted, United dominated the first half, but failed to make their chances pay as strikers Billy Sharp and David McGoldrick missed superb opportunities.
Swansea were poor before the break, but improved after manager Graham Potter introduced Dan James for Wayne Routledge, who had a calf injury.
James made a big impact and Swansea scored the only goal of the game in the 65th minute.
Nathan Dyer played a neat one-two with Mike van der Hoorn and crossed for McBurnie, and the former Bradford City and Barnsley man could not miss.
United goalkeeper Dean Henderson produced two superb saves from Bersant Celina and James, and Swansea held on.
Potter praised his Swansea side’s second-half reaction although his mood was tempered by the news defender Joe Rodon will be out for six weeks with a broken metatarsal suffered in the early stages.
“We struggled to get any real fluidity in the first 20 minutes,” Potter said. “For the second half I just asked the players to play better. In fairness they did. In the second half I thought we were really good.”
Swansea City: Mulder, Naughton, van der Hoorn, Rodon (Carter-Vickers 21), Roberts, Fer, Grimes, Dyer (Fulton 81), Celina, Routledge (James 46), McBurnie. Unused substitutes: Nordfeldt, Montero, McKay, Baker-Richardson.
Sheffield United: Henderson, Basham, Egan, O’Connell, Baldock, Norwood, Fleck (Madine 74), Stevens, Duffy (Dowell 66), Sharp, McGoldrick (Clarke 81). Unused substitutes: Coutts, Stearman, Johnson, Moore.
Referee: John Brooks (Leicestershire).