Adams, who was up against his former club, is still yet to record a win since he took over at Bramall Lane and the 1-0 defeat - courtesy of Andy King`s early strike - leaves his side in the relegation zone.
But he must be left wondering what he has to do after the Foxes were indebted to some excellent saves from goalkeeper Chris Weale to deny the Blades who laid siege on the visiting goal, but are now without a win in eight games in all competitions.
Adams said: "It's one of those nights, a sloppy goal conceded. What can you say? I thought we were the better team but for some good goalkeeping, a bit of good fortune. We definitely should have had a penalty when (Sol) Bamba handled it in the second half.
"But that's football. In terms of the effort and the application, I can't fault the boys, I wish I could. I wish I could go into the dressing room and rip their heads off but I can't after that.
"We've dropped into the bottom three and it's how we respond now. We've got to pick ourselves up, if we have any less application than we've shown here then we'll get beat wherever we go, but I think we're making strides."