United's victory over Everton on Sunday means City are 12 points behind with just 12 games remaining, and Mancini expects a response.
Roberto Mancini: "It's not always the fault of the manager.
"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."
"For a team like us which has won the title, won the FA Cup, won the Charity Shield after 38 years, it's normal the year after as champions could be difficult.
"But probably because we did some mistakes in the summer and we didn't improve our team. But now we have good players and I think we shouldn't do a match like this.
"But in this moment we should do more because we have 12 games, we should get the maximum points we can get, we have the FA Cup and this season is not finished.
"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.
"Usually, we play well and even when we don't play well we put everything on the pitch but we didn't even for that.
"That's the problem. Only this.
"They played better than us, they deserved to win, congratulations to Mauricio Pochettino, to Southampton, but I am very disappointed with our performance."
Source: Manchester City MAD