Mackay's position has come under fresh doubt this week after club owner Vincent Tan sent him an e-mail requesting him to stand down or be sacked.
Mackay is certain that he will not be walking away from the job and enjoyed strong backing from the away fans who chanted his name - and held up 'Tan out' banners - long after the final whistle at Anfield.
"I won't be walking away," Mackay told BT Sport. "That's the first thing. I'm proud to be the manager of Cardiff City."