Substitute Odion Ighalo's 89th-minute goal secured his team's spot in the next round on an afternoon when Forest had acquitted themselves very well against their Premier League opponents.
Jamie Ward had missed an excellent chance to open the scoring seconds before half-time and Forest were unable to beat Costel Pantilimon on a blustery, bracing day.
Jorge Grant and Chris Cohen were handed starts, while David Vaughan returned from suspension to partner Gary Gardner in central midfield.
Oliver Burke was given another starting berth, providing width in an attack spearheaded by captain Dexter Blackstock. Kelvin Wilson and Jack Hobbs lined up in central defence.
On the bench for Forest were Bojan Jokic, Michael Mancienne, Matt Mills, Ben Osborn, Nelson Oliveira, Tyler Walker and Ben Osborn.
Forest took control of the game from the off and Jamie Ward claimed their first shot, cutting in from the left on eight minutes and dragging the ball wide of the post.
Both defences were looking difficult to penetrate in the opening exchanges, with speculative, off-target efforts from Gary Gardner and former Red Adlene Guedioura the final action of note in a cagey opening 20 minutes.
Cohen was looking assured at left back and he did brilliantly to control Vaughan's lofted pass before brushing off the attentions of Allan Nyom on 25 minutes. He progressed down the flank and crossed low for Blackstock who, with Craig Cathcart close by, could only send the ball wide on the slide.
Dorus de Vries was called into action for the first time shortly afterwards, comfortably dealing with Guediora's well struck effort from 20 yards.
A trickier save followed two minutes later when Ikechi Anya pounced on Cohen's mis-control to race into a dangerous shooting position. De Vries got down well to parry the ball away.
New Watford signing Nordin Amrabat was the next to test the Dutchman, firing the ball straight at him from the edge of the area, before Forest regained control as the half neared its conclusion.
Burke controlled Lichaj's low cross in the area and, tightly marked with his back to goal, the winger had little option but to backheel the ball. It neither hit the target nor found the feet of the nearby Blackstock.
One minute of added time was indicated at the end of a half which looked destined to end without a goal.
But, with the last kick before the break, Ward worked himself a golden opportunity to put The Reds ahead. The winger robbed right back Nyom and ran goalwards with the ball. After taking it across the edge of the area to open his angles, Ward opted to surprise Pantilimon at his near post but sent the ball just wide.
The sides emerged for the second half unchanged and it was the visitors who first came close to breaking the deadlock. The ball dropped nicely for Amrobat just outside the area and he struck it beautifully towards de Vries' top corner. The keeper dived to his left to make a superb save, scooping the ball away and behind.
Forest's response came from Gardner, who showed good feet in a tight situation 25 yards out. He had to take his shot quickly and the ball was always angling away from goal.
The match saw its first booking on the hour as Ward was penalised for a foul on Ake down the left, and four minutes later a dangerous move developed down the opposite flank.
Anya did brilliantly to wriggle away from Vaughan near the corner flag. He crossed it low for Amrobat, who met it with a clever flick at the near post. De Vries would have been stranded had the Moroccan found either corner but, thankfully for Forest, the ball rolled straight to the keeper.
Forest's first change came on 68 minutes when Osborn replaced Ward, and that was followed by Watford's introduction of top scorer Ighalo and midfielder Juan Jurado. Anya and Troy Deeney came off.
The game was opening up as it entered its latter stages but both sides were finding it tough to carve out clear-cut opportunities. Eric Lichaj tried his luck for Forest with 11 minutes to go, watching the ball bounce in front of him before sending it dipping goalwards. It dropped straight into Pantilimon's grasp.
Dougie Freedman's next change saw Oliveira replace Grant with eight minutes to go.
And Oliveira's strike partner Blackstock had a chance to win it in the dying moments when Cohen picked him out with a low, whipped cross. The striker couldn't adjust his body to ensure a clean contact with his shot, however, and he sent the ball wide.
Instead it was Watford who would be the beneficiaries of some late drama. Wilson's miskick in his own area presented the ball to Ighalo six yards out and the substitute made no mistake in guiding it past the helpless de Vries.
Forest were given four additional minutes in which to find an equaliser, in the first of which Oliveira burst beyond Watford's back line to latch on to a long ball forward. The Portuguese international went down under a challenge in the box but the referee didn't award a penalty. Osborn kept the move alive, winning a corner which came to nothing.
There was one more glimmer of hope for Forest when Oliveira offloaded the ball to Osborn with space in front of him. The midfielder took it to the edge of the area but didn't strike it cleanly, presenting Pantilimon with an easy save to ensure his side's safe passage into the fifth round.
Forest: De Vries, Lichaj, Wilson, Hobbs, Cohen, O.Burke, Gardner, Vaughan, Grant (Oliveira 83'), Ward (Osborn 68'), Blackstock (c)
Subs not used: Evtimov, Jokic, Mancienne, Mills, Walker,
Bookings: Ward 60', Lichaj 90'
Pantilimon, Nyom, Prödl, Cathcart, Ake, Watson, Guedioura, Abdi, Deeney (c) (Ighalo 72'), Anya (Jurado 72'), Amrabat (Paredas 86')
Subs not used: Gomes, Britos, Holebas, Behrami,
Booking: Amrabat 81'
Goal: Ighalo 89'
Referee: Neil Swarbrick
Attendance: 24,703 (3,771 away)