Everton have been fined £300,000 over the two pitch invasions during their Premier League win over Crystal Palace at Goodison Park on 19 May.
The hosts fought back from 2-0 down to secure their Premier League survival in the penultimate game of the season.
Fans came onto the pitch to celebrate Dominic Calvert-Lewin's 85th-minute winner and after the final whistle.
The Football Association said fans used "threatening and violent behaviour" as they invaded the pitch.
Everton admitted failing to control the crowd.
Premier League clubs announced earlier this month that fans guilty of anti-social or criminal behaviour at top-flight grounds will be banned from attending games at their club for at least a year.
Disorder is at an eight-year high in England and Wales according to Home Office figures, after capacity crowds returned following the end of Covid-19 restrictions.
After the game, Palace manager Patrick Vieira appeared to be involved in an altercation with an Everton fan as he made his way to the away dressing room.
Merseyside Police spoke to both Vieira and the supporter and, along with the FA, took no action over the incident.