The defeat for the Blades leaves them six points from safety and Adams felt his side should not have been on the end of another defeat.
Relegation to League One now looks a real possibility for United, especially after 12 games without a win, but Adams believes his side should not be written off just yet.
He said: "Certainly for the last 15 minutes that wasn't a game that we should have lost. But how many times have we said that since I've been here? I'm absolutely gutted, don't get me wrong.
"Once again it was a set-piece. Obviously those are our Achilles heel. Everyone could see the boys were trying.
"If I'm being critical, it was that we didn't test their keeper enough. We put enough balls into the box but we didn't have enough people attacking them or anticipating where the ball might fall.
"Obviously morale is going to be affected. But morale can change very quickly. Everyone will be writing us off and I can understand that. But we're not dead and buried yet. Not by a long chalk."