Darren Ambrose's second-half stunner left Adams still searching for his first win in 10 games since he took charge of the club he supported as a boy.
More importantly, the Blades are now five points adrift of Palace, and safety, and staring at third-tier football for the first time in 22 years.
Adams said: "The wait goes on, not only for me but for the team.
"I'm sure I'll get plenty of attention but I'm not worried about me, I'm worried about the team.
"But don't write us off yet, we are not finished. I've taken on clubs in worse situations - Fulham were 91st in the pyramid and Coventry in the bottom three."
Source: PA
Source: PA