The Blades were denied a win by an injury-time equaliser scored by Enes Unal.
"It's been a tough week and we have to take that responsibility," Wilder said. "We just had to do so much better.
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"We talked about how ruthless this division is and there's been a lot of pain running through the group and the only way you answer that is attitude over ability, attitude over everything. I'd imagine every neutral would say it was a bit smash and grab but I think after Monday night a sympathetic eye will allow us that point that we fought really hard for.
"It was never going to be a game that we dominated possession but we felt that the longer we grew into it we could catch Bournemouth on the counter. I'm not embarrassed about that; a lot of teams do it."