Bramall Lane has been a reliable place to pick up three points for the Blades this season, but they had to settle for one as they were denied by a combination of poor finishing and goalkeeper Costel Pantilimon.
The hosts' top-scorer Leon Clarke had the pick of the chances in the first half but he unbelievably missed the target with a header from inside the six-yard box.
United pushed on in an attempt to grab all three points and Forest countered them several times but on-loan Chelsea goalkeeper Jamal Blackman pulled off some eye-catching saves to deny Kieran Dowell, Daryl Murphy and Ben Brereton.
Wilder, whose side are two points off a Championship play-off place, said: "We didn't deserve to win it. We didn't show enough quality in the final third and when we did, we've missed chances.
"First goal is massive, especially with our record when we've gone in front here, which is pretty good. I think we've won all our home games when we've scored first so, yeah, it was a bit frustrating.
"Towards the end we're chasing the game because we're not sat in mid-table, we're not just seeing a season out, we've got something to play for.
"We end up trying to do things, change things, putting a forward on, putting another forward on then the game becomes stretched and to be fair the goalkeeper's made a couple of good saves to keep us in the game.
"Maybe some supporters are frustrated that we've not won and I am. The players are but we aren't up against a mug side, are we?"