The Blades missed the chance to reclaim Championship top spot after losing 2-1 at Pride Park on Saturday night.
They were caught cold when Derby’s Craig Bryson scored inside just 19 seconds but then took control, dominating possession, and levelled through Chris Basham before the break.
Frank Lampard’s side improved in the second period, however, and Jack Marriott, their £3m summer signing from Peterborough, nipped in between two defenders to steer home Craig Lawson’s cross in the 77th minute.
“It’s a great result for Frank and Derby and a poor one for us,” admitted Wilder. “It was a tight game between two really good sides and they found their moment. Whether they’ll think it’s a great cross and a fantastic finish, I should imagine so.
“From our point of view, we have to stop the cross and one centre forward has got in between two of our centre halves so that’s a really poor goal for us to concede. The lad shouldn’t have that space and time in the box as he did and Kieron Freeman should get out to stop the cross.
“(But) I didn’t see it coming. I didn’t feel as if we were really massively under the cosh. I just felt as if it’d be a game that would be won by a bit of a magic or a mistake.”
Wilder felt his side - who host Stoke City tomorrow - should have made more of their first-half chances. He knew they would respond after that early setback.
“I didn’t expect anything different,” he said. “The players have really good character. Anyone who has seen this group over the last two or three years will know there was no doubt about it that they’d react positively.
“To go behind so quickly is a big blow but I thought we were really good and we should have found that last bit at the end to go in at half-time up in the game. We didn’t do that. We had enough possession, had enough territory and got around the back enough times - we got around the back more than they did to us second half – but that final little bit wasn’t there.
“Countless times in the first half we moved the ball around their two full-backs and got into some great positions without the final ball.”
Wilder added: “Derby were better than us second half. I’ve no complaints about the second half and the result overall because if you defend like that and don’t put teams to bed in the first half the result can go either way.”
United almost levelled again when Scott Carson dropped a cross and Jack O’Connell’s header was cleared off the line by Mason Mount. It was a high-quality game for the neutrals to enjoy and certainly a fine advert for Championship football.
But Wilder insisted: “From a Sheffield United manager, I don’t give two ***** what the neutrals think. I knew that was coming. I understand that. But we’re losing footballers. Regardless of what opposition we’re in. If we were winning footballers and it’s three points then I still wouldn’t be bothered – all I’m bothered about is us.”