The Red Devils opted to part company with Mourinho last week after the Portuguese coach paid the price for their disappointing start to the Premier League season.
Manchester United lost 3-1 to Liverpool FC at Anfield in his final Premier League game in charge as the Red Devils produced a below-par performance on Merseyside.
Mourinho’s big-name players such as Paul Pogba, Romelu Lukaku, Alexis Sanchez and Eric Bailly struggled to produce consistent performances under the former Real Madrid boss.
Keane’s former team-mate Ole Gunnar Solskjaer has taken over the reins of the 20-time English champions on an interim basis before Manchester United look to make a permanent appointment at the end of the season.
The ex-Manchester United captain criticised some of the Red Devils players for their cowardly approach in the media and their poor performances on the pitch.
“You would fall out with these players,” Keane told BBC Radio 5 live.
“Players who turn up overweight, do not train properly and are not producing… for some to down tools, shame on some of those players.
“I am not Mourinho’s biggest fan, but I can’t tolerate footballers who hide behind agents, their pals in the media – it is a bit of a joke.”
Keane added: “The players got away with murder. They hide behind the manager. They have thrown him under the bus.”
Manchester United haven’t launched a sustained title challenge since Sir Alex Ferguson won his 13th top flight crown in his final season in charge of the club in 2013.
The Red Devils have appointed David Moyes, Louis van Gaal and Mourinho as their permanent managers since Ferguson’s retirement but the trio have all struggled to revive their fortunes.
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