Last season's champions are just one point outside the relegation zone this term, with prospects of a top-four finish already looking slim.
A 2-1 defeat at Leicester on Monday night was the latest blow to the Blues and manager Jose Mourinho.
Now Fabregas says there can be no excuses as Chelsea attempt to turn around their season.
"We all have to take responsibility
If you are a big player and you are paid like a big player, you must play like a big player and behave like a big player," Fabregas said in a Facebook interview
"I am not saying you can't have a bad season and bad games
We all have - big players and small players
But the attitude has to always be spot on
We must always be at the top of our games, and the behaviour has to be better than what we are seeing right now from every single Chelsea player."
Mourinho accused Chelsea stars of betrayal with their performance at Leicester, who went to the top of the table with their victory.
The manager's strong views on the display will have been noted by Chelsea's players, and former Arsenal and Barcelona man Fabregas has called for extra effort over the remainder of the season.
Fellow strugglers Sunderland are the visitors to Stamford Bridge on Saturday, and Chelsea risk falling into the relegation zone if they suffer another poor result.
"We cannot win the Premier League right now, but come on, we all have to do better," Fabregas said
"Right now is not the time to think of where we might finish, we've been saying it nearly all season.
"I just think I want to beat Sunderland, play my best and that's it
Right now, no one is easy as it shows
We've put ourselves in this position so we have to now prove - we really, really, really have to now start winning."
Source : PA
Source: PA