United's U21s slipped to defeat against Premier League opposition on Thursday afternoon.
A goal in each half from Freddie Ladapo secure all three points for Crystal Palace, despite a spirited performance from United's young side, which included Louis Reed and three trialists.
The result means the Blades still need a point from two remaining matches to ensure a top two finish and a play-off berth.
The Eagles took the lead in the eighth minute when Williams released LADAPO and the striker finished first time past Eastwood.
The visitors response was almost immediate though with De Girolamo having a couple of attempts on goal, but the Blades went in at the interval behind.
United came out in a positive manner in the second period, but despite enjoying the majority of the ball, goalscoring chances were at something of premium, although Brooks volleyed over from inside the penalty area.
And with 25 minutes remaining, Palace doubled their advantage, as LADAPO hit an unstoppable shot past Eastwood with the ball going into the net off the post.
The Blades again looked to mount a comeback, but the Premier League side stood firm, despite a flurry of United corners, to condemn John Dungworth's side to a second consecutive defeat, having previously gone 16 matches unbeaten in the Professional Development League.
But Dungworth said there were positives in the performance, despite the loss, remarking: "We were poor by our high standards against Colchester and didn't deserve anything from the game.
"But our endeavours against a good Palace side deserved more than we got. It is a learning curve for these young players though, because it proves you have to make your possession count and remain tight defensively.
"We played very well overall, but were punished for losing the ball in bad areas, whilst at the other end despite numerous crosses and corners; we failed to score when on top."
Blades: Eastwood, Charlesworth (Cummings 45), Brown, Gilmour, Oseni, Semple, L'Ghoul (T. Smith 51), Reed, Ndjoli (Hall 74), De Girolamo, Brooks.
Unused: Ramsdale, Hallam.