Former Leeds United striker Steve Morison’s 89th-minute penalty secured victory for Millwall at The Den.
The result leaves Wilder’s side bottom of the League One table, and he said: “It’s disappointing for everyone at the football club. One point from four games isn’t good enough.
“We started well and went behind against the run of play, and showed great steel to get back in the game and dominated the first half.
“But when you’re on top, you have to put teams to bed and (failing to do) that has been the downfall for us.
“I’ve let the players think about their own performances, think about what’s happened over the last four games and we’ll make a more sensible appraisal on Monday.
“If you’ve been involved with this club and you feel a lot about the club, as I do, you get very emotional about the start we’ve had.
“I need to take myself out of that situation and make a more considered approach on Monday because one point out of four games is not good enough and we’re all hurting.”
Thirty-two-year-old Morison coolly tucked away the spot-kick after Jack O’Connell’s handball in a thrilling climax. Shaun Williams and Stefan Scougall had traded first-half goals.
Millwall: Archer, Romeo, Webster, Craig, Martin, Worrall, Thompson, Williams, O’Brien (Ferguson 70), Gregory (Onyedinma 82), Morison. Unused substitutes: Wylde, Nelson, Abdou, Philpot, King.
Sheffield United: Moore, Freeman (McNulty 90), Wilson, O’Connell, Hussey, Scougall (Chapman 82), Coutts, Basham, Duffy, Sharp (Done 65), Clarke. Unused substitutes: Ramsdale, Wright, Kieran Wallace, Whiteman.
Referee: Andy Woolmer (Northamptonshire).