Speculation over the Scot's future has been rife since the dismissal of Iain Moody as head of recruitment last month.
Moody was hired as Crystal Palace's sporting director on Saturday, leading Mackay to be linked with the managerial vacancy at Selhurst Park.
But, speaking after his side's 2-0 defeat to Aston Villa on Saturday, the Scot insisted he remains committed to Cardiff and has no intention of walking away.
"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 the result at Villa Park, Mackay was full of praise for his side - especially his defenders.
"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.
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