Forest could have made it 5-1 when Max Lowe steered a left-footed effort from the edge of the box just wide of Ward’s far post after 66 minutes.
But while Forest continued to threaten, Leicester failed to create any chances of note as they watched their hold on the FA Cup slip away in highly disappointing fashion.
Amartey tried to make amends for his earlier error with a fizzing left-footed volley from outside the box that Samba held smartly down to his right, and Ricardo Pereira sent a low shot just wide after dribbling into the area, but Forest were relatively untroubled as they backed up their third-round win over Arsenal with another spectacular win against top-flight opponents.
As for Leicester, they exited the tournament with a whimper at the hands of their East Midlands rivals and now have just five wins from their last 18 matches from all competitions.
Captain Joe Worrall returned for Forest after missing the last three matches with a broken rib
Keinan Davis replaced top scorer Lewis Grabban, who scored the winner in the last round against Arsenal but is out for the next two months with an ankle injury
New signing Sam Surridge was named on the bench for Forest
Danny Ward started in place of Kasper Schmeichel in goal for Leicester
Wilfred Ndidi and Kelechi Iheanacho started after returning from the Africa Cup of Nations following Nigeria’s last-16 exit
Johnson: I never wanted to leave Forest
Brennan Johnson’s outstanding performance – including his third goal in his last four matches – demonstrated why Brentford wanted to make him their record signing last month.
But the 20-year-old insisted he was keen to remain at his boyhood club during the transfer window, telling BBC Sport after the game: “I love this club and I always wanted to stay, the whole window.
“Once January the 31st finished I was just focused on finishing the season here.”
Johnson also praised the impact of Steve Cooper, who replaced Chris Hughton in September. The former Swansea boss has taken from Forest from the bottom of the Championship to the verge of the play-offs, and said: “He’s just told us to always believe in the way we play, especially against Premier League teams.
“We showed it against Arsenal. Ever since then we’ve just wanted to believe in ourselves. We know we’re a good team.”
The ties will be played in the week commencing Monday February 28, 2022.
Nottingham Forest travel to face Blackburn in the Championship on Wednesday at 7.45pm, live on Sky Sports Arena. Liverpool host Leicester City in the Premier League on Thursday at Anfield at 7.45pm.