The Premier League champions made it three consecutive games without a win after losing 3-1 to Southampton at St Mary's on Saturday.
City are now 12 points behind Manchester United in the table, and Mancini believes that the players need a snappy response.
"When you play football and you are a top player, you should take your responsibility, always," said Mancini.
"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."
City host Chelsea in their next match on February 24.