Postecoglou's miserable 39-day reign at the Midlands side came to an end 20 minutes after the full-time whistle as the Australian became the first Forest manager to fail to win any of his first eight games in charge.
The speed of the dismissal caught even the players off guard as Postecoglou was sacked even before he could fulfil his post-match media duties, with the 60-year-old leaving The City Ground immediately after speaking to the team.
'Everybody has to take responsibility'
"I'll be honest. Ange came in after the game, debriefed the game and then I went out to do some running. I came back and news had broke that he had gone," Yates told BBC Radio.
"Everybody has to take responsibility. I think it would be unfair to pin it on anybody.
"We have to look ourselves in the mirror and dust ourselves down and go again because things in football can change really quickly. That's what we are going to be thinking about."
Following other results on Saturday, Forest have now slipped into the relegation zone, sitting 18th with five points after eight games - two points behind Burnley in 17th.
No wins for Forest since season opener
Without a win in any competition since their season opener, including the Europa League, where they are 25th in the standings, Forest are looking for a third manager to take charge this season after Postecoglou replaced Nuno Espirito Santo.
"Partly we are to blame (for Postecoglou's sacking) because we are the guys going out on the pitch and trying to get results," Yates added.
"Things in football can change very quickly. With a good result on Thursday night (against Porto in the Europa League), we can get that good feeling back and we kick in."
British media reported former Burnley and Everton boss Sean Dyche is in the frame to come in and steady the ship, while Roberto Mancini, who guided Manchester City to their first Premier League title, is an option for the beleaguered club.