City were defeated by the Saints on Saturday in a game in which they showed little fight or spirit.
“I don’t want to see a player like we saw. A player who plays like that should stay at home, not even be on the pitch,” said Mancini.
“Usually, we play well and even when we don’t play well we put everything on the pitch. We didn’t do this. That’s the problem for today. Only this.
“When you play football and you are a top player, you should take your responsibility. Always. It’s not always the fault of the manager.
“The players should take responsibility – if they have big balls. If not, they can’t play in a top team. We can lose if a team plays better than us. That’s normal. But not like this.”