The Scotland international takes heart from Palace’s performance in the second half of last season when they beat Liverpool, Arsenal and Chelsea on their way to winning eight of their last 16 matches to safeguard survival.
Zaha is out of action for at least a month and the Eagles’ record in his absence is poor as they have not picked up a Premier League win without him since September 2016.
“He is a big loss. He’s a big player for the club but it is about every one of us sticking together and stepping up to try to fill that void of Wilfried,” McArthur said.
“We are going to work hard and make sure that we do everything. Everyone will make sure we do a job and that will be good enough.
“Every game is tough in the league. You would have said that last year where we picked up a lot of amazing results against the big teams, so hopefully we go on a run this season and do the same thing.
“They will definitely be big points. We need to concentrate on the next game now, rectify what we did wrong and make it right.”
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.
Southend manager Chris Powell led the applause for Jason Demetriou after the right-back scored twice in the 3-1 win against Portsmouth at Roots Hall.
Morecambe boss Jim Bentley was the happier manager after Gregg Wylde's 90th-minute strike earned his side a point in their 1-1 draw with Forest Green.
Manager Gareth Ainsworth described Wycombe's 2-0 win at Cheltenham as a thoroughly professional performance.
Skipper Richard Wood scored the winner just before half time as in-form Rotherham pulled off a 1-0 victory at League One leaders Shrewsbury.