A little more than a week after manager Colin Calderwood was fired, Forest stunned City with goals from Nathan Tyson, Rob Earnshaw and Joe Garner.
Forest is fourth from the bottom in its return to the League Championship after three seasons in the third-level League One.
"The aim is to get this club back where it once was," said 20-year-old Lewis McGugan. "The name Nottingham Forest speaks for itself. The history is there for everyone to see. We should not be where we are but results like this will just build confidence even more. Hopefully, we can go on a run of games now and start picking up points in the league, which is the proper stuff for us."
City's loss increased the pressure on its manager, Mark Hughes. The Welshman hopes to use the January transfer window to get reinforcements. The loss to Forest marked the eighth time in the last nine games City has failed to win.
"I'm trying to be honest and I've known from day one the frailties of the team," said Hughes, who was without star Robinho. "When we play well and everyone shows the same desire, we are a good team. But when we're off the pace, then we're not."
Forest's victory sets up a date with another former English league champion, neighbor Derby County.
U.S.-owned Derby County, only three places above Forest in its return from the Premier League, twice trailed non-league Forest Green (2-0 and 3-2) before coming back to win, 4-3.
Adding to the drama of the Forest-Derby match is that former Derby manager Billy Davies replaces Calderwood as Forest's manager on Monday.
The big match on tap for the fourth round will be the Merseyside derby between Premier League leader Liverpool city rival Everton, which has not given up a goal in its last five games.
They met in the 1986 and 1989 FA Cup finals, and Liverpool won both times.
"It's going to be a massive game," former Everton captain Kevin Ratcliffe. "The FA Cup is one that maybe Everton thought they could go all the way in. Obviously, this has made it a bit harder, coming up against Liverpool."
Liverpool vs. Everton
Manchester United vs. Tottenham Hotspur
Hull or Newcastle vs. Millwall or Crewe
Sunderland vs. Blyth Spartans or Blackburn Rovers
Hartlepool vs. West Ham
Leyton Orient or Sheffield United vs. Charlton or Norwich
Cardiff vs. Arsenal
Portsmouth or Bristol City vs. Histon or Swansea
Chelsea or Southend vs. Ipswich
Cheltenham or Doncaster vs. Aston Villa
West Brom or Peterborough vs. QPR or Burnley
Torquay vs. Coventry
Kettering vs. Fulham
Watford vs. Leicester or Crystal Palace
Derby vs. Nottingham Forest
Birmingham or Wolves vs. Middlesbrough
Third-round replays: Jan. 13
Fourth round: Jan. 24-25