Today's 5-1 thrashing at Newcastle confirmed the Blades are down.
Wilder said: "It (relegation) stings and it hurts. We have to own it. We have got so much work to do on the training ground. We have got to have a proper pre-season.
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"Sheffield United is a really good football club. I think everyone understands that but it's been a really poor season.
"I've still got another year left of my contract. I'd like to think that the supporters can trust me. I'm enthusiastic and committed along with my coaching staff to get it right. We know exactly what direction we need to go, what the culture is going to look like, what pre-season is going to look like.
"It's going to be a tough summer for everybody."