Defending champions Liverpool fell behind in the 33rd minute when Murillo’s fierce strike punished their failure to deal with Elliot Anderson’s corner.
Reds boss Arne Slot was fuming that the goal was allowed despite Forest’s Dan Ndoye appearing to obstruct Liverpool keeper Alisson Becker — an offence that led Virgil van Dijk’s equaliser to be disallowed in the 3-0 loss at Manchester City before the international break.
Sean Dyche’s side doubled their lead after 46 minutes when Nicolo Savona slotted home from Neco Williams’ cut-back.
With Liverpool’s defence in disarray, Morgan Gibbs-White scored Forest’s third from the rebound after Omari Hutchinson’s shot was saved in the 78th minute.
Beaten by Forest at Anfield for a second successive season, Liverpool have lost eight of their last 11 games in all competitions, including six of their last seven in the top flight.
It is the first time Liverpool have lost consecutive league games by a three-goal margin since 1965.
Once again Liverpool were devoid of inspiration and energy in another lethargic display that left them languishing in 11th place, eight points behind leaders Arsenal.
“Another big disappointment. We started off quite well but we conceded the 1-0 and weren’t able to play the way we did in the first half hour,” Slot said.
“If things go well or things go bad, it’s my responsibility. We weren’t able to create enough. I tried to adjust a few things, but it didn’t work out. We are in a very bad spell.”
At St James’ Park, Manchester City trailed to Barnes’ 63rd-minute drive from the edge of the area before Ruben Dias equalised with a deflected strike five minutes later.
Two minutes after Dias levelled, Barnes bagged Newcastle’s contentious second goal with a fierce volley, which was allowed to stand after a lengthy VAR check for a potential offside against Bruno Guimaraes, whose header had cannoned back off the bar.
Guardiola was also aggrieved over a rejected first-half penalty claim by Phil Foden.
City’s fourth league defeat this season left them in third place, four points behind Arsenal, who host local rivals Tottenham on Sunday.
Guardiola stormed onto the pitch at full-time to confront referee Sam Barrott, but later insisted “everything is fine” when asked about the incident.
“It happened in the Bournemouth game and it happened today again. It is what it is after VAR decided. They know perfectly,” he said of Newcastle’s second goal.
“It was entertaining game, we both had chances and then there was a momentum shift and ultimately we couldn’t win.”
Chelsea moved up to second place with a 2-0 win at Burnley.
Pedro Neto’s diving header put Chelsea ahead just before the interval and Enzo Fernandez netted in the closing stages.
Enzo Maresca’s side, who sit three points behind Arsenal, have won eight of their last 10 matches in all competitions, making it a memorable 50th Premier League game in charge for the Italian.
New Wolves manager Rob Edwards suffered a 2-0 debut defeat against fourth-placed Crystal Palace at Molineux.
Brighton came from behind to defeat Brentford 2-1 at the Amex Stadium.
Raul Jimenez’s 84th-minute goal gave Fulham a 1-0 victory against Sunderland at Craven Cottage.
West Ham blew a two-goal lead in their 2-2 draw at Bournemouth. (AFP)
