A 4-0 defeat away to Tottenham in their last match suggested there is still much room for improvement.
And Zaha told HLTCO: "As much as I do on the pitch, I can't play in every position.
"I give 100 per cent, but there are 11 on the pitch and everyone needs to pull their weight."
As for the transfer speculation during the close-season, the Ivory Coast international added: "What happened in the summer happened… there were things I was told that did not happen and I was not happy about it. But I'm still a Palace player and want to do well for the club.
"The fans care about your wellbeing and I will always love Palace - whatever happens."