The 39-year-old was named caretaker manager at the club last week after the Rovers board sacked Richie Wellens following a poor start to the League One season, especially away from home.
At the Keepmoat Stadium on Saturday afternoon, Branden Horton put the home side, who were in desperate need of a morale-boosting win, ahead after just seven minutes.
That remained the only goal come half-time, as Doncaster were unable to turn their dominance with the ball into clear-cut chances.
They would soon be made to pay.
Will Forrester equalised within three minutes of the restart and Mansfield went on to establish a two-goal lead through a brace from George Lapslie.
That proved crucial for the visitors as Tommy Rowe reduced the deficit to a single goal but the Stags held on to upset their hosts.
The defeat means Rovers have exited two knockout competitions in less than a week, after they were beaten in the Papa John’s Trophy by Crewe Alexandra last Wednesday.
“We’re disappointed not to get a result,” reflected McSheffrey.
“We came out aggressively in the first half, pressed them well, forced errors and with a bit more quality and cutting edge in possession and decision-making we could have gone in at half-time two or three up.
“More cutting edge and maybe a bit more energy in the final third, we could have maybe been more comfortable.”
McSheffrey felt that his side failed to cope with the introduction of Mansfield’s Jordan Bowery, who was brought on for the second half.
“They made the change at half-time and for 15 minutes or so we didn’t have an answer,” added the caretaker chief.
“There comes a point when you have to take responsibility as individuals.
“We had three experienced defenders on from the start but it came to the point where I had to move Tommy Rowe out of there because I needed him higher up the pitch.
“You could see the momentum Mansfield had and we needed to respond to that. Once they got one, it was hard to stop that with the run they’re on as well.
“We need to be smarter with how we play, too.”
Victory would have secured Rovers £34,000 in prize money and put them in the third round draw alongside every Premier League and Championship club.
“That was the aim. It would have been nice,” added McSheffrey on missing out on a third-round place.
It is another short turnaround for Rovers, as they prepare to host Oxford United tomorrow night as they look to improve their position in the League One table.
Oxford are just one place outside the play-off spots but McSheffrey’s focus will be on instilling some confidence in a downbeat squad.
When asked how he would go about that, he responded: “You have to be upbeat. You show them clips of all the positive things we did and be constructive of the things we could have done better.
“Then you go to preparing for Oxford and how we feel we can exploit them.
“On a good day, they can beat anyone in this league quite comfortably. On a bad day, they can get some really erratic results as well.
“Tough times don’t last. Some of the boys maybe need a bit of perspective. There is no time to feel sorry for ourselves, we have got work to do.”
Doncaster Rovers: Jones; Knoyle, Anderson, Rowe, Horton; Ravenhill (Blythe 57), Smith, Hasani; Barlow (Cukur 64), Dodoo, Hiwula. Unused substitutes: Dahlberg, Faulkner, Cole, Henson, Wilds, Kuleya.
Mansfield Town: Bishop; McLaughlin (Bowery 46), Hewitt, Clarke (Charsley 90), Maris, Quinn, Oates (Sinclair 80), Forrester, Stirk, Lapslie, O’Toole. Unused substitutes: Shelvey, Burke, Ward, Law, Mason.
Referee: S Stockbridge (Tyne and Wear).