With five games remaining, starting today at the Proact Stadium (1pm), the Blades trail sixth-placed Gillingham by nine points.
Even a maximum haul of 15 points – United have home games against Barnsley and Scunthorpe plus trips to Shrewsbury and Coventry to come – may not be enough for a top-six berth.
But Adkins is demanding maximum effort from his players, and a repeat display after Blades fans applauded the team off – despite a 0-0 draw with the Gills – following last week’s impressive performance.
“It’s been a frustrating season,” admitted Adkins. “Everyone is working hard to make things happen. We are building, but ultimately it’s about winning games.
“The players are working hard and we ain’t taking our foot off the pedal.
“We are still pushing for as much as we can to get ourselves in the play-offs.
“It’s a big ask, but we can just focus on the next game.
“Chesterfield is going to be a full house, it will be passionate, and I anticipate it will be full-blooded. We have to give the supporters something to cheer about.”
United come up against some familiar faces at the Spireites, with former Blades duo Danny Wilson and Chris Morgan now in charge at the Derbyshire club.
Adkins said: “It will be a good game. Danny and Chris Morgan are two Sheffield United legends. They are at the opposite end of the table, but it’s a derby game. They are good football people.”
Former centre-half Morgan – a legend at Bramall Lane in his time as a player, coach and even caretaker boss on two occasions – said: “I had 12 and a half fantastic years there and it’s a club that will always be in my heart, but now I’m Chesterfield Football Club’s first-team coach and I’m a professional fellow.
“The gaffer’s an ex-Sheffield United manager, he’s an utter professional as well and we now represent Chesterfield.”