Postecoglou, 60, was sacked after just over a month in charge of Nottingham Forest, losing six and drawing two of his eight game at the helm.
Forest have since replaced him with former Burnley and Everton manager Sean Dyche, who took charge of his first game against FC Porto in the Europa League on Thursday (October 23).
Keane, who spent time at the club as a player and then an assistant to Martin O’Neill, has since hit out at the players for being the reason Postecoglou got the sack.
Speaking on the latest episode of The Overlap, he said: "You look at the Forest players and the chances they had. What chance has he (Postecoglou) got?
“Did they really want to score? Did they want to keep them in the job? I'm on about good players not even hitting the target.
“Then the manager loses his job, you look at these Forest players, and they're like, ‘oh well, another manager has gone, a new one comes in, you know’. Idiots, honestly."