The Owls frustrated the hosts to secure a derby point in a 0-0 draw when victory would have seen the Blades return to the top of the Championship.
The hosts were left to rue a 15th-minute penalty miss from David McGoldrick, with Sheffield-born keeper Cameron Dawson guessing right to make a vital save as the Owls claimed a precious point to ease the pressure on under-fire manager Jos Luhukay.
Wilder said: “I was delighted with the way we played. It shows how far we have come.
“We pegged a team back who were in the play-off semi-final two seasons ago and the play-off final and resorted to just booting it anywhere.
“They have big-hitters and big-name players and wages.”
Luhukay added: “You are always happy when you are not losing games and the draw was very important for us and we got a clean sheet for the first time.
“At the beginning of the game, we had some luck and Cammy stopped the penalty at a very important moment.
“Cammy was fantastic. We all forget that we are playing with a very young goalkeeper. This was maybe his biggest game and he did a really good job.
“I don’t really understand why he has had a lot of critics.”