The Blades – who travel to Brentford tomorrow – missed the chance to go top of the Championship after twice being pegged back by the Millers in a pulsating derby at the New York Stadium.
“Our performance just wasn’t good enough,” said Wilder. “We didn’t deserve anything out of the game. We seemed to think we could just stroll in and it would be a pretty easy afternoon.
“We were naive in our play and the players didn’t recognise that Rotherham would be on top of them. Maybe I need to get that message across more strongly. We didn’t have time and space to take touches.
“They were hungrier than us and off they went. Rotherham played more effective football. I imagine they had more ball than us, more crosses, more shots. They did to us what we usually do to other teams.
“It is up to me now to look at that and then make the relevant changes for Tuesday (at Brentford). I usually enjoy our performances in and out of possession but I didn’t enjoy that.”
Wilder’s fury was in stark contrast to the satisfaction Paul Warne took from his side’s battling display.
Jamie Proctor came off the bench to rescue a point for the hosts in stoppage time and the Millers chief said: “We took the game to them and deserved our equaliser.
“At 2-1 down, I was disappointed but I was still proud of the performance. The lads could not have given me any more. They went toe-to-toe with one of the best teams in the league. To get the equaliser so late on made it feel like a win.”
Proctor’s late leveller saw the Blades drop to fifth in the table but Yorkshire’s other promotion hopefuls had a better afternoon with Leeds United beating Bristol City 2-0 and Middlesbrough triumphing 2-1 at Griffin Park.
Kemar Roofe and Pablo Hernandez scored in the final quarter for Leeds to break the resistance of a Robins side reduced to ten men by Josh Brownhill’s 55th minute dismissal.
Marcelo Bielsa said: “When I see the game again I’ll take into account this point of view – that we didn’t deserve to win the game. At the beginning of the second half and from minutes 25 to 35, we didn’t dominate.
“For the rest of the time we dominated. “The fact that we played with one player more made it easy for us but I don’t think it was the only argument.”