A battling display could not prevent United slipping out of the FA Cup at Bolton on Sunday.
Goals from Paul Coutts and Jack O'Connell were not enough to book a place in the third round draw.
Boss Wilder made five changes for the tie - Ramsdale, Hussey, Scougall, Lavery and Brown all started. Chapman, who scored a hat-trick in the demolition of Leyton Orient in the first round, missed out after picking up an ankle injury on Friday.
The opening half hour was entertaining, despite a lack of goals. Bolton were the first to try to force an opening but Ameobi scuffed wide and then Scougall headed wide a Hussey cross.
United looked to get on top but efforts from Freeman and Lavery were blocked and then Ramsdale was called upon to keep the Trotters out. The teenager goalkeeper acrobatically pushed wide a Madine shot but then did better from the resulting corner. On 29 minutes, from Spearing's delivery, Ramsdale kept out both Beevers and Madine before Brown kicked Wheater's effort off the line.
The chances continued as half-time approached. Clough curled wide for the hosts and Scougall sidefooted a volley wide after Freeman had headed down a Coutts cross, before the home side snatched the lead close to the break. Taylor's long throw was flicked on by Wilson and MADINE hooked home at the back post despite the efforts of Ramsdale and Basham.
Bolton netted with the last chance of the first half and the first chance of the second. Less than a minute after the restart, a low cross from the left saw AMEOBI curl into the bottom corner of Ramsdale's net from 18 yards.
United had an opportunity to reduce the arrears moments after but Alnwick recovered to save from Freeman after dropping Hussey's cross. Wilder threw on Duffy but strikers Clarke and Lavery picked bookings.
The Blades, however, were handed a lifeline on 64 minutes. With little other option, captain COUTTS tried his luck from 25 yards and a deflection saw the effort drift past Alnwick's left hand into the net.
Ramsdale saved Freeman after Clough nipped in to cut out a back header, whilst at the other end Freeman headed over a Fleck corner.
In the final 15 minutes Madine scuffed at Ramsdale after Clough broke the offside trap before Bolton added third. VELA played a one-two with Clough to open up the Blades defence before slotting past the exposed Ramsdale.
United hit straight back. Sharp, on as a late substitute, crossed for Clarke and although his effort was deflected wide, the visitors netted from the resulting corner. Fleck's delivery saw O'CONNELL get a run in his marker to head home at the near post.
Four minutes of added time saw United pressing. A patient move ended with Alnwick collecting Freeman's cross and with a crowded box Coutts overhit his delivery.
United were unable to created one more chance and defeat leaves Chris Wilder with just the league to concentrate on for the remainder of the season.
Bolton: Alnwick, Beevers, Vela, Spearing, Clough, Madine (Proctor 84), Taylor, Ameobi (Taylor 82), Wilson, Wheater, Thorpe (Osede 75).
Unused: Buxton, Moxey, Anderson, Turner.
Blades: Ramsdale, Hussey, Fleck, O'Connell, Basham, Scougall (Sharp 84), Lavery, Brown (Duffy 49), Coutts, Freeman, Clarke.
Unused: Done, Reed, Whiteman, Lafferty, Moore.