Palace have endured a torrid start to the campaign, losing their first seven games without even scoring a goal to leave them rock-bottom of the pile.
However, following the appointment of the experienced Roy Hodgson as manager, winger Zaha is sure the Eagles will turn it around soon.
"I'm very confident," he said. "We've got good enough players but it's just a thing where if you don't have the confidence then you can't play like yourselves.
"Soon enough we will go back to ourselves. We've got a good enough team and I think we'll get out of this position."
Zaha has also given his opinion why Frank de Boer, who was sacked after just four games in charge at the start of the season, didn't get results at Selhurst Park, claiming that he tied to change their philosophy quickly and turn to a more possession-based game - something the players weren't used to.
"He (De Boer) wanted to make Palace into a team that had more possession," he added on BBC Sport.
"But obviously some players aren't as comfortable on the ball as he would like. That didn't really help us at the time.
"There wasn't really the right mixture (of players) for the way we wanted to play."