The Tigers were the better side for majority of the first-half and deservedly went into the break with a two goal advantage. Jarrod Bowen gave the home side the lead as he prodded home via the woodwork after getting the better of Michael Mancienne. The hosts were able to double their advantage shortly before half-time as Nouha Dicko headed home from close range.
Forest did manage to pull a goal back two minutes from time courtesy of a fine finish from Apostolos Vellios but it was too little too late as the Reds were knocked out of the FA Cup early on once again.
Bowen lights up first-half for Tigers
Aitor Karanka made one change to his starting line-up from the one that beat league leaders Wolverhampton Wanderers 2-0 at Molineux last weekend and it was a forced change. Mustapha Carayol came in for the suspended Liam Bridcutt who was given a two-match suspension following his tenth booking of the season against Wolves last weekend.
It was Forest who had the first opportunity of the match as Carayol fired a right-footed shot narrowly wide of the target from distance. However, this was one of very few chances that the away side managed to create in the first-half.
Forest keeper Jordan Smith had to be alert to tip Markus Henriksen's low driven free-kick round the post for a corner. He was almost beaten minutes later following a mix-up with Joe Worrall which almost allowed Bowen to lob the ball into the back of the net but his effort bounced back into play off the post.
However, the Tigers did get the goal they deserved soon after through Bowen. The forward got the better of Mancienne as he drove towards goal and his shot found the back of the net via the post much to the delight of the home supporters.
Andreas Bouchalakis had been a key player in Forest's victory over Wolves last weekend but was struggling to have an impact in this one as he repeatedly lost possession.
The Reds were made to pay for their sloppiness shortly before half-time as Dicko doubled the host's advantage. Danny Fox was beaten at the far post too easily by Bowen who headed back across goal for Dicko to flick the ball into the back of the net from close range.
Forest did have one big opportunity to pull a goal back before the break but Carayol scuffed his effort wide from close range when he should have scored. This saw Nigel Adkins' side head into the break with a well deserved two goal cushion and it could have been more.
Late Vellios strike not enough for Forest
Karanka recognised that he needed to make changes at half-time and he decided to bring on David Vaughan and Zach Clough for Carayol and Bouchalakis.
Forest came close to getting the early goal that they needed in the second-half through Everton loanee Kieran Dowell. His free-kick had David Marshall beaten but it cannoned back off the post.
The away side were desperately trying to find a way back into the game which did leave them open at the back and left them vulnerable to the counter-attack. Worrall was next to test Marshall as his header was tipped over the bar superbly by the Tigers keeper.
Forest's 18-year-old striker Ben Brereton had a superb game in the 4-2 victory over Premier League side Arsenal in the previous round and came so close to getting his side back into this match. He got the faintest of touches on Dowell's cross but his effort bounced away off the post, much to the despair of Forest's large travelling support.
Karanka decided to introduce Vellios with around ten minutes to go as the striker made only his second appearance for the Reds this season. It did not take him long to make an impact as he volleyed Matty Cash's cross into the back of the net to give the away side a glimmer of hope with a few minutes left to play.
However, it was too little too late for the away side as they crashed out of the competition early on yet again. As for Hull, they will be hoping that they can secure a 'glamour tie' in the next round as a distraction from their recent struggles in the league.