Already relegated, Ferguson had called for his side to give their supporters a “decent send-off”.
But Ferguson said: “The players should be embarrassed [about this season], we all are. But we are totally up for the challenge of getting back in League One.
“It’s been a horrible week for us and we all know it’s going to be a long summer. But we will meet with the board on Tuesday and assess the challenge of [trying to] bounce back up.”
Lucas Adkins headed wide from Andy Butler’s corner after only seven minutes as the Brewers went close to an early lead. It was the 34th minute before the next chance as Tom Naylor headed over from Mark Duffy’s corner.
Five minutes later Matthew Palmer forced a smart save from Rovers’ Remi Matthews.
Rovers failed to create any clearcut chances in the first half, but did have a penalty appeal turned down just before the break after the ball looked to have struck a Burton player’s arm.
Craig Alcock went close to breaking the deadlock five minutes after the restart, but his powerful fight-foot shot was well-saved by Jon McLaughlin.
Rovers had a great shout for a penalty in the 65th minute after Andy Williams looked to have been felled in the area, but again referee Andy Woolmer waved away the home side’s protests.
Doncaster Rovers: Matthews, Lund, Alcock, Butler, Taylor-Sinclair, McCullough, Middleton (Calder 54), Chaplow (Longbottom 62), Rowe, Williams, Mandeville (Tyson 53). Unused substitutes: Marosi, Pugh, Whitehouse, Davies.
Burton Albion: McLaughlin, Edwards, Mousinho, Cansdell-Sherriff, McCrory, Choudhury, Akins, Naylor (Weir 79), Palmer, Duffy, Beavon (Butcher 45). Unused substitutes: Reilly, Myers-Harness, Walker, O’Connor, Bywater.
Referee: A Woolmer.