Zaha returned to Selhurst Park after being deemed surplus to requirements at Manchester United this summer.
"We needed to add more firepower," Delaney is quoted as saying by the London Evening Standard. "I was delighted when Wilf came back because he has that X factor you are looking for.
"He's not up to full speed yet but he nearly scored against Burnley. Then it is up to the rest of us dogs to see the game out.
"The manager wants to be a bit more attacking and has brought in players who will help give us that without losing solidity."
Zaha made his Crystal Palace Premier League debut against Newcastle United, scoring a late equaliser to earn the Eagles a point.