The Welsh club, in their first Premier League match at home, scored through Aron Gunnarsson and Fraizer Campbell (double) in the second half after Edin Dzeko had put City ahead and then Alvaro Negredo gave them late hope.
But the Bluebirds saw out the contest to pick up an early win in their debut Premier League campaign and Mackay was thrilled with how much impact the fans had on the outcome.
"When the goals went in it was something quite incredible," he said.
"The stadium, the team, the staff and the fans did us proud today in front of a worldwide audience.
"The passion the people have got for this showed when the goals went in.
"It is something that is going to be massively important for us going forward. They are our 12th man."