The Bluebirds lost their opener 2-0 at West Ham and the Blues hammered Newcastle United 4-0 under new boss Manuel Pellegrini.
Mackay said: "You see the way that team played, they are warming to their new manager quite quickly.
"So we realise the task in hand."
Having dominated the 2012-13 Championship on their way to the top flight and not lost at home since February of last season, Mackay hopes home fans will be as influential this time around.
But not all Cardiff City fans are happy despite a full house guranteed. Fans opposed to City's change of shirt colour from blue to red plan to celebrate the club's heritage ahead of the Manchester City game.
Organisers of the Bluebirds Unite walk from Cardiff Castle to the stadium say it is not a march against the club.
Malaysian owner Vincent Tan changed the club's colour to "lucky" red last year as part of his investment and made the bluebird less prominent on the crest.
Sian Branson from Bluebirds Unite said: "We are trying to do something positive. It's celebrating the history and heritage of the Welsh capital's football club.
"We can't understand the reason for the rebrand but we are not marching against the club or saying 'Tan Out'.
"It's the first game in the Premier League and we are not being represented on the pitch as our club and we're trying to show what it means to us.
"Why should everything before last year be forgotten.
"We hope the owner will take notice and see it's a mistake and we can have it rectified for next season."
The group hopes around 1,000 fans will turn up for the walk which starts a couple of hours before the match itself.
Tan first put in £6m at the club after being asked by his friend Dato Chan Tien Ghee, the former chairman of Cardiff City, around three years ago.
Initially he was in the background as an investor but after loaning the club more than £30m, he decided to play a far more active role when he saw Cardiff lose in the Championship play-offs at the end of the 2011-12 season.
His first move was to carry out the controversial rebrand in an attempt to gain popularity for the club in Asia.
Last month, Tan said: "If too many fans show that we are not welcome then maybe they will have a new owner but right now my experiences are that we are very welcome."