Wilder returned to Bramall Lane to replace the sacked Ruben Selles this week and will now be acutely aware of the scale of his task after substitute Tanto Oloafe's goal consigned his side to a sixth defeat from six matches in the second tier.
Tyrese Campbell missed two good chances in the first half but Sheffield United keeper Michael Cooper denied Lloyd Jones and Greg Docherty headed over for the visitors before Oloafe turned home a low cross in the dying seconds.
"We've got a bit of work to do," Wilder, who has previously managed Sheffield United in the Premier League, told the BBC.
"There are some bits and pieces out there I was pretty pleased with, but there's a lot of stuff that definitely needs some work on the training ground."
City rivals Sheffield Wednesday claimed their first win of the campaign as Barry Bannan's early free-kick and a second-half strike from George Brown gave the Owls a 2-0 win at Portsmouth.
Stoke lost 1-0 at QPR, missing the chance to put pressure on Championship leaders Middlesbrough, who are four points clear at the top of the table after their 2-1 win against West Brom on Friday.
A superb goalkeeping display from Coventry's Carl Rushworth helped Frank Lampard's men hold on for a goalless draw at Leicester.
Preston beat Derby 1-0 to climb into the Championship play-off positions.
Blackburn's game against Ipswich was abandoned about 10 minutes from time due to heavy rain at Ewood Park.
Ipswich had Jacob Greaves sent off four minutes into the second half and Blackburn led 1-0 due to Todd Cantwell's penalty.
The pressure eased on Wrexham boss Phil Parkinson as a Josh Windass double helped his side secure a 3-2 win over Norwich at Carrow Road.
Hull ended a run of three games without a win, easing past Southampton 3-1 and Birmingham overcame Swansea 1-0.