The Scot's position has been under scrutiny since his head of recruitment Iain Moody was removed from his role.
But Mackay says he has no intention of leaving the Cardiff City Stadium as he prepares his side for Saturday's trip to Aston Villa.
"We are all working to ensure Cardiff City is again playing top-level football next season," he said.
"I want to be talking to the media in a year's time as Cardiff City manager in the Premier League.
"We relish being in the Premier League in terms of players and fans. Our aim is to be the best we can be and finish as high as we can.
"I am proud to be manager here. We have worked hard as a staff for two-and-a-half years to take our beliefs forward, mould our squad to the point we have reached now.
"We will keep moving forward and make sure everything we do is for the best of Cardiff City. I will always do my best and that will never change."