Costa and Fabregas were both booed off when substituted, with fans chanting the name of Jose Mourinho at Costa, who looked furious.
Some fans did also applaud Fabregas, but boos were prominent.
Costa denied he was unsettled in the summer when reports emerged linking him with a move back to Atletico Madrid.
But he has yet to learn English and, following an explosive start, has endured a miserable year with a mere 11 goals in 2015.
Fabregas has lived in London for much of his life and would surely be more inclined to ride out the abuse, even though his position would be untenable if it persists.
The crowd also directed chants at the entire home team, singing, 'Where were you when we were s***' when the team went 3-0 up.
Captain Terry, who made a point of applauding the fans from the centre circle at the end of the much-needed win, claimed supporters had every right to feel aggrieved.
'Absolutely and rightly so as well,' he said. 'Chelsea is such a big club. We're not used to being here - the last ten years we've had a lot of good times.
'They'll support us through this difficult period and we'll come out on top sooner or later. If we keep on putting in performances like that then the fans will be going home happy with smiles on their faces.
'But rightly so - they're disappointed and so are we. We don't want to be where we are.'
But Terry did urge the supporters to lay off Costa and Fabregas, claiming the responsibility lay with the entire team.
'I think all of us are in this position - it's not one or two individuals and that's me speaking honestly,' said Terry. 'We're all in this position because one or two have performed and the rest haven't, unfortunately.
'That's behind us now, it's in the past and we have to move on. We need to start winning football matches and Chelsea need to be a lot higher in the league than we are.'
Holland, who took charge of the first team on Saturday, claimed that the players could win back the fans at Stamford Bridge.
'If the players play and compete as they did here, I don't see any reason why the supporters wouldn't be happy with that,' he said.
Holland made a point of applauding both the underfire Spain players as they left the pitch when substituted.
He said: 'Thinking of this game, I was happy with their contributions so I applauded them when they came off.
'I am happy with the result but it is raw - I feel the way I feel. During the first half, we played well in general.
'The early goal gave the players a boost of confidence, but the team is still fragile to an extent. We are used to setbacks in recent weeks so we wobbled a little bit in the second half. I thought we saw the game out fairly comfortably.'
- Daily Mail