Nigel Clough admitted he was frustrated at seeing his team not secure their play-off spot, following the 1-1 draw with Bradford City on Saturday.
Former United loanee Billy Clarke equalised late on for the Bantams after Jason Holt's opener looked to have secured the win needed for the home side, coupled with Rochdale losing at Gillingham.
But the point means that Keith Hill's side can still overhaul the Blades if they win all three of their remaining fixtures and Clough's side lose against Leyton Orient and Chesterfield.
Speaking in the aftermath of the stalemate at Bramall Lane, the Gaffer remarked:
"We have still got that nagging doubt, it is an unlikely set of circumstances as it stands but you never know in football.
"We now have to wait until Tuesday and possibly beyond that to next Saturday to confirm our top six spot, but with five or six minutes to go it was the ideal scenario, we were winning and Rochdale were losing but in the end it didn't quite happen for us."
Clough thought his side had done enough to beat Phil Parkinson's City: "We were good in possession at times without doing too much in the final third, although after we had gone in front, for 10-15 minutes we really looked liked getting that decisive second goal.
"I thought defensively we looked comfortable throughout, even after losing Terry Kennedy.
"Chris Basham dealt excellently with James Hanson, but when they put as many balls into the box as they did then one could always drop and it is a soft goal to concede for us having defended so well with a patched up back four.
"We struggled to settle and play our own game for long enough periods, whilst we had to work very hard to stop Bradford."