The announcement regarding Postecoglou's dismissal was made less than 20 minutes after the final whistle.
In reaction, Hoddle commented on Forest owner Evangelos Marinakos, saying: "To leave his seat after 60 minutes was a statement in itself. I'm surprised he has done it so quickly after the game."
Hoddle also suggested that Postecoglou should have been given more time to turn the team's fortunes around, stating: "Eight games is no time at all. Surely he has got to be given more time than that."
Former Chelsea winger Pat Nevin also shared his thoughts on the situation, describing it as a "wild shambles". He added that owners should occasionally take a closer look at their own actions and decisions, saying: "I do think eight games, even though it's been bad, that ain't enough to see if you are good enough."