The 41-year-old, who was relieved of his duties following the 3-0 defeat to Southampton on Boxing Day, hopes his departure does not have a negative impact on the club's season
The Scot was relieved of his duties on Friday following a turbulent festive period which saw him allegedly given an ultimatum by owner Vincent Tan to resign or be sacked.
Mackay, who guided the club to promotion to the Premier League by winning the Championship last season, insists he is already able to reflect on the good times he spent at Cardiff.
"It is with the deepest and most sincere regret that I today confirm my sacking as manager of Cardiff City," read a statement from the 41-year-old.
"As disappointing as today's decision is, I am already able to look back at my time at Cardiff City with immense pride and joy given the number of milestones the club achieved during the last two and a half years.
"A League Cup final appearance followed by promotion to the Premiership for the very first time, achieved as winners of the Championship, allowed the club a move back to this elite level after a 51-year absence."
And Mackay expressed a desire for his successor to enjoy a calmer reign than he has had to endure this campaign.
"I would like to thank my players, all of my direct footballing staff, all the people behind the scenes at the club," he added.
"And most importantly the people of Cardiff, who have stood behind me resolutely throughout my time here and especially in these recent turbulent months.
"I leave with my head held high having gained a level of experience that, upon reflection, I suspect would have been difficult to find anywhere else in British football.
"The foundations laid at Cardiff City will provide a solid platform for my successor, and for the sake of the club, I hope that all of the progress that has been made so far will not be impaired in any way by today’s enforced changes."