The Reds dominated the opening 30 minutes but after going behind they looked out of ideas as Forest left Anfield deserved winners. Liverpool have now lost six of their last seven league games.
The decisions did not have a huge impact on the end result.
Everton, meanwhile, were also involved in a controversial decision as they were able to overcome a major piece of adversity to beat Manchester United on Monday night. Idrissa Gueye was sent off early into the game for a confrontation with team-mate Michael Keane - but the offence did not appear worthy of a red card.
“When I saw it I didn’t think there was anything in it,” Moyes said afterwards. “I was a bit annoyed they were challenging each other but I was also quite pleased they were fighting each other because it shows me they cared.”
However, Kiernan Dewsbury-Hall fired in a stunning goal on 29 minutes as Everton kept United at bay to claim a hugely-impressive win.
With VAR continuing to cause contention, we have worked out how the current Premier League table would look without the technology.
Points without VAR: 2
1. 20th: Wolves
Points without VAR: 2 | Getty Images
Points without VAR: 10
2. 19th: Burnley
Points without VAR: 10 | AFP via Getty Images
Points without VAR: 11
3. 18th: West Ham United
Points without VAR: 11 | Getty Images
Points without VAR: 12 (+1 point)
4. 17th: Leeds United
Points without VAR: 12 (+1 point) | Getty Images