The NRL came down hard as it issued the Eels with a $AU10,000 breach notice, which the club has five days to respond to.
According to a statement from the NRL, Stuart's comments breached guidelines which prevent a coach questioning the integrity of the referee, from engaging in criticism that is excessive or unjustified or from ridiculing officials.
"Coaches are allowed to question or criticise decisions but there are some clear boundaries that every club should be aware of,'' NRL general manager of football operations Nathan McGuirk said.
"We believe that on this occasion those boundaries were breached.''