Nuno has been fined £40,000 and handed a one-game touchline ban, which is suspended until 31 May 2026, while Williams has been fined £24,000.
It follows their comments after Forest had three penalty decisions go against them in their 2-0 Premier League defeat at Goodison Park in April.
Nuno said the officials had “bad” games while Williams told Sky Sports: “Every single week this happens now. We are getting decisions against us, I don’t know why. Is it because we are a lower, bottom half of the table team?”
Both men have also been warned about their future conduct.
As part of the Premier League’s commitment to improving VAR, BBC Sport understands the league has spoken to clubs and managers about the impact of public criticism of VAR undermining the game – and that there will be a new focus on regulating these public comments.
Sources told BBC Sport the Premier League felt it became too easy to blame VAR as a deflection.
On the pitch, there were 12 manager touchline bans last season.
The FA said in a statement: “It was alleged that the manager and player’s comments constitute improper conduct in that they implied bias and/or questioned the integrity of the match officials and/or bring the game into disrepute.”
A decision by the FA against the club is still to be made, however, after Forest released an angry statement on X – seen over 45m times – just minutes after the final whistle.
The club claimed they told referees body the Professional Game Match Officials Limited (PGMOL) that the game’s video assistant referee (VAR) Stuart Attwell was allegedly a fan of relegation rivals Luton.
The fallout from the game also led to former Premier League referee Mark Clattenburg leaving his role as a referee analyst at Forest.
Clattenburg, in the Mail on Sunday, called the decisions a “joke” and said Forest were “feeling victimised “.