Jürgen Klopp’s men set up a semi-final clash with Manchester City at Wembley next month thanks to a solitary Diogo Jota strike 12 minutes from the end at the City Ground.
Team news
The Reds made seven changes for the trip to the east Midlands, with only Alisson Becker, Virgil van Dijk, Fabinho and Jota retaining their places from the midweek Premier League win at Arsenal.
Liverpool: Alisson, Gomez, Konate, Van Dijk, Tsimikas, Fabinho (Thiago, 64), Keita (Henderson, 64), Oxlade-Chamberlain (Minamino, 64), Elliott (Diaz, 64), Jota, Firmino.
Unused substitutes: Adrian, Jones, Origi, Matip, Beck.
First half
The game began at a fast pace with both sides exchanging attacks in the opening period.
Forest posed the first threat of the evening in a game which failed to settle into a rhythm following the first whistle, Joe Lolley seeing his low cross cleared at the last moment by Naby Keita.
Liverpool responded as Joe Gomez twice got in behind on the right, before Kostas Tsimikas fired a dipping volley inches over the bar from distance.
Fabinho again threatened thanks to a shot from a low Alex Oxlade-Chamberlain corner but the Brazilian’s effort fell the wrong side of the post.
The home team were starting to play on the counter-attack and another quick break saw Lolley shoot wide from distance following the wide man’s cut in from the flank.
Roberto Firmino, who cleverly beat the Forest offside trap to latch on to a through ball, failed to make the most of the best chance of the opening half as Klopp’s side dominated possession.
The attacker found himself one-on-one with Ethan Horvath, though his dinked finish from inside the area was saved by the onrushing goalkeeper.
Gomez struck another thunderous effort goalwards as the opening period came to a close but his half-volley flew over the bar, leaving the two teams to enter the break level.
Second half
Similarly to the first 45 minutes, Forest started with a purpose; however, it was the Reds who had the best chances to begin the second half.
Jota first saw a curling shot saved from the edge of the box, before Oxlade-Chamberlain’s low drive deflected perfectly into the hands of Horvath.
As the game reached the hour mark, Klopp responded by making a quadruple substitution and introduced Luis Diaz, Takumi Minamino, Jordan Henderson and Thiago Alcantara from the bench.
Forest worked a golden chance to open the scoring with the game entering the final 15 minutes, but Philip Zinckernagel failed to find the back of the net from the penalty spot as he watched his low strike fly past the far post.
The Dane was left all alone inside the area and was made to pay for the miss just minutes later as Jota opened the scoring for the Reds.
Tsimikas whipped an inch-perfect ball to the back post and the forward was on hand to prod home into the back of the net.
Forest saw a late penalty claim waved away after Ryan Yates fell inside the box as Alisson rushed out to greet his forward run. The midfielder also saw a free header from a Brennan Johnson cross saved by the goalkeeper with time ticking down.
But Jota’s late strike proved enough to see Klopp’s outfit edge into the final four of the competition for the first time under the Reds boss, with City up next at Wembley.
Attendance: 28,584