The Eagles had not won a match without the Ivory Coast international in two years until a 1-0 victory over Leicester in December.
Zaha sits out this weekend’s derby after a lack of discipline saw him earn a second booking for sarcastically applauding referee Andre Marriner in Wednesday night’s 1-1 draw at Southampton.
Further punishment could follow as he did not leave the field of play quickly.
“We believe we can win any game, no matter who is playing,” said McArthur.
“He is one of our best players in the team and we will miss him.
But we have got players in the squad that hopefully are ready to go and take their chance.”