Fans of the West London club jeered the pair as their names were read out before Saturday’s game on the PA system and then when they were substituted towards the end of the match.
They also repeatedly chanted in support of the sacked Jose Mourinho, who has been replaced on an interim basis by Guus Hiddink, and unveiled a banner saying: “You let Jose down, you let us down.”
“I told the players whatever their feelings were regarding the situation, they had a responsibility to the football club and the supporters,” said Holland, who took charge of the team with Hiddink watching from the stands.
“We have quality players and they care. I’m not a social media guy so I’m not sure of the exact reasons, but clearly the supporters have a right to voice their opinion. I’m happy to park this and move on.
“I’ve not spoken to those players. From my point of view I was happy with their contribution to this game and applauded them.
“If the players compete like they did today, there will be no reason why the supporters won’t be happy with that.”
Goals from Branislav Ivanovic, Pedro and Oscar, with a penalty, saw Chelsea end a three-game winless league run against the backdrop of a peculiar atmosphere.
Holland believes that Mourinho will be back in management before the end of the season after the Portuguese expressed eagerness to return to work in a statement released by his agents.
“I think he will be back before the end of the season,” said the former Crewe Alexandra manager.
“Big clubs will want him and I think he is someone who needs and wants football. He is not someone who will spend six, seven, eight months doing nothing in particular.”
Holland added: “I don’t know what the circumstances are contractually. He will want to get going sooner rather than later and it would not be a surprise if big clubs are interested in him.
“Jose has invited me out for a meal next week. Our relationship is excellent. He would recognise I gave him everything. Not only is he an exceptional manager, but is an exceptional person.”
Chelsea were 2-0 up after just 13 minutes courtesy of Ivanovic’s header and Pedro’s emphatic finish, while a third arrived from Oscar’s 50th-minute penalty after Costel Pantilimon brought down Willian.
Fabio Borini pulled one back from close range three minutes later.
Former Chelsea player Didier Drogba also watched from the stands alongside Hiddink and owner Roman Abramovich, but a club source said he was there purely in support of his old teammates.
Sunderland manager Sam Allardyce was frustrated by his side’s performance and admitted that he may now look to the January transfer window in an attempt to stave off the threat of relegation.
“I think we made it really easy for them by giving a goal away from a corner and that allowed their confidence to grow,” he said.
“The only good thing is we never laid down and died. We came back and made Chelsea a little nervous, but never looked like getting the result. That’s very disappointing. It’s a big worry in terms of where I go next.
“I’ve had a while to look at it and I’m disappointed with a lack of consistency. We’ve dropped right back into the mire.
“I think we let them turn the style on. I’m disappointed we did not make a better show of themselves. The team under-performed and they have to do better.
“I have to find a solution. If I can’t find the solution within the squad, I will have to find it in January.”
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