Supporters have yet to embrace their new home with sections of the London Stadium chanting "we should have stayed at the Boleyn" during the recent 1-1 draw with Middlesbrough.
Sullivan wrote on whufc.com: "Despite our frustrating start to the season, the fans have been fantastic".
The Ghana global was substituted just 34 minutes into his Premier League debut for Slaven Bilic's side and is not expected to be available for the first-team until late November.
"Palace have started the season really well, but we have to get something, and I expect us to get something from the game".
West Ham, who finished seventh under Bilic last season, now sit in 18th, and know that they must improve quickly if they are to pull away from the relegation zone.
"I am sure I'll be telling the lads at Palace all about them".
"Crystal Palace didn't start well, but the last four games they have got ten points and they probably didn't want the break". I can't put my finger on why they have been struggling.
Bilic promised to launch an investigation into the events, but admitted he hasn' t made too much progress.
The previously balding Bilic - whose hair was noticeably thicker on top than last month - said: "When something happens off the pitch I need to know the whole story and I don't know it so far".
They are likely to have James Tomkins playing for them and I have to say that we needed to do more to try and keep him at the club.
"I'm going to react but it isn't done and I don't think about that at the moment, I am thinking about our next game".
Bilic will be boosted by the return of left-back Aaron Cresswell following a knee injury and he added that long-term absentees Carroll, Diafra Sakho and Andre Ayew are also nearing a return to action.