“It shouldn’t have been a nail-biter,” said Wilder.
David McGoldrick’s double condemned the Lions to a seventh Championship game without a victory, despite Billy Sharp missing a first-half penalty.
The Blades striker atoned to score the opener but Jake Cooper and Lee Gregory found the net for the hosts within the first five minutes of the second half.
Yet Millwall crumbed as McGoldrick scored a penalty and then netted with two minutes to go.
Wilder continued: “We had to be right at it. For five minutes we weren’t and we got punished. But for the majority of time we were and we all played our part in what I believe was a deserved victory.
“If we’d have walked away with two each I would have been delighted with the way we played. Credit to them.
“The momentum went, the place was rocking and it changed from being a comfortable afternoon to one that was difficult.
“I’m just glad we don’t have to come here again because it is such a difficult place to play at. No doubt they’ll get a result and they’ll be up and running.
“They’re a tough team no matter how you look at it. They’ve got too many good players, too many honest professionals that want to run around and get a result.
“Millwall will find a way to win, without a shadow of a doubt. We’re delighted with 19 points after 10 games but that can quickly change if things aren’t right.”
Millwall remain stranded in the relegation zone after McGoldrick tucked home from three yards two minutes from time, after scoring from the penalty spot 10 minutes previous after a foul.
Sharp had earlier put the Blades in front, atoning for missing his own spot-kick thanks to a wonderful save from Ben Amos following a handball.
But, after the home crowd made their feelings heard at half-time, Cooper headed home from a corner just two minutes after the restart to level the contest.
Gregory then ran onto a ball over the top and finished on 50 minutes but United battled back.
Millwall: Amos, Romeo, Webster, Cooper, Meredith (Bradshaw 89), Jed Wallace, Williams, Leonard, O’Brien (Ferguson 80), Morison (Elliott 84), Gregory. Unused substitutes: Archer, Tunnicliffe, Murray Wallace, Skalak.
Sheffield United: Henderson, Basham, Egan, O’Connell, Freeman, Norwood, Fleck, Stevens (Johnson 75), Duffy (Stearman 90), Sharp, McGoldrick (Clarke 90). Unused substitutes: Washington, Lundstram, Coutts, Moore.
Referee: A Davies (Hampshire).