United's Under 23s conceded two late goals in their final Premier League Cup match against Everton which means they're now relying on Doncaster to get a result against Blackburn on Monday night.
Reece York's header had put United ahead with half an hour to go but a late strike from substitute Bassala Sambou and a stoppage time strike from Manasse Mampala sealed Everton's spot at the top and denied the Blades assured progression into the last 16.
On a difficult pitch, the first half was a very quiet affair with neither side able to mount any major chances.
United were lively down the wide areas and sent in several dangerous crosses but were forced into a change shortly before the break when Kyron Gordon replaced Keenan Ferguson.
The second half saw more chances as Everton introduced Sambou and United went after the goal that would assure them qualification and top spot in Group B.
Jake Eastwood made a big save to deny Sambou on the hour and it was a big moment when the Blades went instantly down the other end and took the lead.
A corner in found Reece York unmarked at the back post to head the Blades into the lead with just under half an hour remaining.
But Everton stepped it up a gear in the late stages, Eastwood again forced into a save from Josh Bowler before Sambou eventually had the desired effect with just over five minutes remaining.
Bowler's low cross found Sambou and the striker did the rest, with Everton putting the game to bed with the final attack of the game in stoppage time.
Bowler was again the creator, sliding in Mampala who turned his man and fired a low effort past Eastwood to seal the game for the hosts.
Blades: Eastwood, Ferguson (Gordon 40), Belehouan, Broadbent, Bennett, York, Sheppeard, Neal, Oure, Greaves, Boyes.
Unused: Dewhurst, Gomis, Ackroyd, Young.