Forest are reportedly aggrieved that Fulham were awarded their winning penalty by VAR while they were denied two spot-kicks by reviews in Stockley Park.
The FA charged Nuno Espirito Santo and Neco Williams for improper conduct over comments made after the game while Mark Clattenburg left his role as the club's referee advisor with a warning.
As per The Telegraph, owner Evangelos Marinakis was 'angered' on Saturday while a senior source said: 'The standard of refereeing is destroying the status of the Premier League and damaging its clubs.
'There appears to be no consistency of decision-making from VAR.
'There still isn't sufficient transparency in the VAR process. It's the fans who suffer too.
'VAR was intended to improve the game for clubs and supporters alike, but it's failing them at the moment.'
Mail Sport has contacted the PGMOL for comment.
Raul Jimenez converted the second-half penalty which ended Forest's unbeaten start to the season. The contentious penalty was awarded after referee Josh Smith went to his VAR monitor, as advised by VAR official John Brooks.
Forest also had two disappointments concerning calls not to award them a spot-kick. In the first half, VAR judged that Joachim Andersen had not fouled Taiwo Awoniyi. In the second, VAR upheld the decision not to award Anthony Elanga a chance from 12 yards after a challenge from Calvin Bassey.
The club's latest outburst, while not released in official form yet, follows their extraordinary statement after the Everton defeat in April.
The Midlands club - in the heart of a relegation battle at the bottom of the Premier League - claimed they warned PGMOL over bias from VAR official Stuart Attwell, a supporter of then-relegation rivals Luton Town.
Three penalty calls the way of Fulham on Saturday, which their spot-kick ending Forest's unbeaten start to the season
This is what they had to say in the wake of the 2-0 defeat by Everton last season, when they were in a relegation dogfight with Luton
On X, the club wrote: 'Three extremely poor decisions - three penalties not given - which we simply cannot accept.
'We warned the PGMOL that the VAR is a Luton fan before the game but they didn't change him. Our patience has been tested multiple times. NFFC will now consider its options.'
This week, Nuno Espirito Santo, captain Morgan Gibbs-White and Brighton boss Fabian Hurzeler were all charged by the FA aftert their red cards in the 2-2 draw last Sunday.
Nuno and Hurzeler were charged with acting in an improper manner, with the Forest boss also accused of using abusive and/or insulting words towards a match official. He could yet face a touchline ban.
'We all want peace and for things to continue well, to not have to speak about the referees. But it was bad, wasn't it?' he said after the game. 'We don't want to talk about it [referee decisions]. Nobody wants to talk about it.
'When we come to the game, we don't think about the referee, we just want to compete and play the game and hope the referee gets things right.'