A first half of few chances saw the Reds enjoy the best of the play, but they failed to take advantage when Fabio Carvalho's effort at Dean Henderson was tame, while Virgil van Dijk's decision to head the ball across the goal despite being 6 yards out saw it travel harmlessly to safety.
Forest looked to hit Liverpool on the counter-attack for the majority of the match, and they enjoyed some success when winning the ball high up the pitch, but no more so than when Taiwo Awoniyi forced Joe Gomez into a mistake in the second half, allowing the hosts to score from the resulting free kick. Their lead was almost doubled before James Milner blocked Morgan Gibbs-White's effort at goal.
Van Dijk had the best chance for the equaliser in injury time as he directed a free header at goal, only for his effort to be matched by Henderson, who produced a strong quick-reaction save to ensure that Steve Cooper's side earned all three points.
A positive performance for Curtis Jones will help Liverpool going forward after a number of injury problems, and it was yet another bright display from Harvey Elliott, who is continuing to shine for Jurgen Klopp.
The Reds were sloppy in possession too often, and that saw forward balls travel carelessly out of play. Liverpool also seemed to have returned to their ways of conceding multiple counter-attacks, eventually being punished by Awoniyi.
Manager rating out of 10
Jurgen Klopp, 6 -- Responded quickly to going 1-0 down with two substitutions that could have been made earlier. Klopp's game plan looked to be enough for the win on the day, but individual errors in decision-making on the pitch meant there was little he could do.
Player ratings (1-10; 10 = best, players introduced after 70 minutes get no rating)
GK Alisson 7 - There wasn't much Alisson could do about the opening goal as it cannoned back off of the woodwork and into the path of Awoniyi. Kept the game at 1-0 with some big saves.
DF Andy Robertson 6 - Often made the right decision when going forward and didn't allow much to develop down his flank, although opponents did seem to be targeting the opposite wing.
DF Virgil van Dijk 6 - An assured performance at the back, but his biggest moment of the game was when he didn't direct his header at goal from 6 yards out. His injury time effort was too central and allowed Henderson to make the save.
DF Joe Gomez 5 - Sometimes took too long on the ball and was caught out in the second half when fouling Awoniyi before the opening goal.
DF James Milner 7- Stretched play on the right channel and looked to overlap Elliott to create chances with crosses into the box. A key block kept Liverpool in the game.
MF Fabinho 5 - Looked to anchor the back four, but he could rarely get close to Forest players to make a challenge. Play broke down too often when he was in possession, with his worst moment when he ran into traffic with the ball and lost it carelessly in the 85th minute.
MF Curtis Jones 7 - Neat in possession in a role that saw Jones look to control the game from the midfield rather than create goal-scoring chances in more advanced areas. A strong performance after some time on the sideline with an injury in a role that could suit him in future games.
MF Harvey Elliott 7 - Elliott looked bright every time he had the ball as the Reds regularly created attacks down the right flank, and he almost picked up an assist with an exquisite pass that provided Carvalho with a one-on-one opportunity.
FW Fabio Carvalho 6 - The 20-year-old had the first big chance of the game with a delicate touch that took down Elliott's pass, but he couldn't get the finish right. Wasteful in possession at times.
FW Roberto Firmino 5 - Liverpool struggled to get the ball to Firmino, who didn't make the most of his limited opportunities in possession. Eventually replaced in the 76th minute.
FW Mohamed Salah 5 - Hesitant with decision-making and couldn't seem to get going overall against Forest's deep back line. Anonymous in the second half after failing to get a proper connection on a chance when he had more time than he thought.
Trent Alexander-Arnold (Milner, 62") 7 - A number of dangerous set-piece deliveries almost led to goals, but Firmino and Van Dijk couldn't convert. Came close with a header to draw a save from Henderson.
Jordan Henderson (Carvalho, 62") 6 - The captain pressed aggressively from midfield to help Liverpool win the ball back in better positions.
Alex Oxlade-Chamberlain (Firmino, 76") N/R - Introduced for Firmino on his return from injury -- his first appearance this season.