Defeat at home to Chelsea left Postecoglou winless in his first eight games in charge of Forest.
An announcement regarding the Australian's dismissal came less than 20 minutes after the final whistle.
Richards said: "It was inevitable but I don't think it's right. He was only given eight games and a contrast of styles was always going to be a factor.
"Forest went from one of the best counter-attacking managers to one who wanted to be more expansive - it was never going to work straight away.
"Ange Postecoglou is a good manager but it's possible his media outbursts haven't helped. It looked like he could have been the right fit but more time was needed.
"The interesting thing now is - will the next manager be short term or long term? What are Forest trying to be - was last season a one-off?
"I know Tottenham finished fifth in Ange's first season but if you're going off Ange's record last season, he should never have been appointed by Forest. Maybe they needed to aim higher in terms of what they were doing and go for a manager with a style they really wanted.
"If you do go for Ange, how can he change their style of play in such a short space of time?
"Now the club could be in panic mode just to stay in the league. If Sean Dyche does turn out to be who they go for, he's always said he'd love an array of talent to work with - and he's got that at Forest."