Mackay's head of recruitment Iain Moody was replaced last week by 23-year-old Kazakhstani Alisher Apsalyamov on an interim basis.
Apsalyamov is thought to be a friend of Cardiff owner Vincent Tan's son and appears to have no previous experience in football.
Moody first worked with Mackay at Watford - initially as press officer and then football operations manager - before leaving Vicarage Road with the Scot and his management team in the summer of 2011 to take up the role with Cardiff City.
Caulker, a summer signing with a transfer fee in excess of £8m initiated by Moody, told Sky Sports News: "The players have not talked about it and there's no bad atmosphere but hopefully now we can concentrate on keeping Cardiff in the Premier League.
"I spoke with the manager before he joined and obviously he works very closely with Iain Moody, they seemed to have a tight bond.
"But I really appreciate him as a manager, I think he doesn't let his feelings be shown and he's led the team in the right way."
On Apsalyamov, the centre-half added: "Yeah I've met him once or twice around the changing room and he's a nice guy."
Caulker scored against Sweden in his only appearance for England in a 4-2 away defeat 12 months ago and admitted he would love to travel as part of the squad to Brazil for next summer's finals.
He said: "It's important for me to have a good year to have any chance of going to the World Cup.
"It's important to keep the faith and believe if you do work hard an opportunity may arise to be in that World Cup squad in Brazil."