The 41-year-old has been linked with a move to Crystal Palace to join his former head of recruitment Iain Moody at Selhurst Park
Speculation over the Scot's future has been rife since the dismissal of Iain Moody as head of recruitment in October.
Moody was hired as Crystal Palace's sporting director on Saturday, leading Mackay to be linked with the managerial vacancy at Selhurst Park.
"I'm the Cardiff City manager and I said that yesterday,” Mackay said.
"I’ve got a great group of players and staff. I’m the manager of Cardiff City and I’m proud to be that."
Despite Cardiff's 2-0 defeat to Aston Villa on Saturday, Mackay was full of praise for his central defensive duo of Steven Caulker and Ben Turner.
"I thought our back five - our two centre-backs especially - were immense today, they were playing against a real handful in the two players they were up against. But I thought they were both immense," he added.