Last month, the Eagles paid Paris Saint-Germain a club-record £10m, rising to £13m with add-ons, for the France international.
Speaking to Sky Sports' Geoff Shreeves ahead of Arsenal's visit to Selhurst Park - live on Super Sunday from 12.30pm on Sky Sports 1 - Cabaye said he wants to repay his manager's faith in him.
Yohan Cabaye: "One day, the manager called me to ask if I would come to play for Palace.
"I was happy because I know the manager and I wanted to come back to the Premier League.
"He is really close to the players. Every player in the dressing room, those who start the game, the subs, even those who are not involved in the game... he is really close to us.
"He knows each player's quality and he gets the best from us. He gives to us the confidence and you just want to give the confidence back to him."