Moody is now sporting director at Palace, having left his role as Cardiff's head of recruitment in October under controversial circumstances.
Moody helped Mackay bring 25 players in to Cardiff during a little over two years together in south Wales, before he was replaced by Kazakh Alisher Apsalyamov.
Mackay has nothing but kind words for Moody, and expects him to make a difference in the long term, but with just the January transfer window ahead, the Scot says it will be new manager Pulis who plays the biggest part if Palace are to survive.
Mackay said: "Iain is a good man and over a period of time will bring a structure to a recruitment department and a common sense approach.
"He ran the recruitment department of the football club here and ran it very well. He spoke to agents and football clubs about players and contracts and had scouts working for him which all filtered into him and then filtered into me.
"It was a good structure and I am sure that is what he will do there."
But when asked if Moody's expertise could help keep Palace in the Premier League for next term, he said: "Tony Pulis is going to be the biggest influence on whether Palace stay up or not.
"Tony is a very experienced manager and someone that does a lot of hard work with his team.
"But it will take him time to mould Palace in the way he wants it."
Moody, for his part, claims he has still not received an explanation for his Cardiff dismissal from owner Vincent Tan.
"I look forward to his explanation because I'm still bereft of any official explanation from him, so it will bring some light on it from my point of view too," Moody told The Guardian.
"I have no doubt that it was his decision. But I have had no direct conversation with him at all since something like August 28, at the end of the window."
Palace's win over West Ham on Tuesday moved them off the bottom of the table and raised hopes that the Eagles can recover from a dreadful start to the season to avoid a rapid return to the Championship.
Cardiff are currently four points clear of the Londoners after their draw with Stoke, and Mackay expects a difficult test against a side given a sudden injection of confidence.
"It's another tough away game," said Mackay. "I get the fact that fans see the Arsenal and Manchester United games as exciting and also there is thought that we were probably not expected to get anything from those games.
"There is a hope we will get something from these other games. I just take it in cold hard facts of how we approach the game.
"Palace have got a new manager and that always brings that little bit of momentum and impetus as far as a group of players are concerned as was shown on Tuesday night.
"But they were never a club that were that far detached. I've watched some of the games they've played on TV and they have not been that much worse than anyone else.
"If you are in this league you are here on merit. There are some funny results that will be thrown up throughout the season."
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