The Staggies began the campaign with a goalless draw at home to last season's domestic cup double winners St Johnstone before defeats away to Hibernian and at home to champions Rangers preceded the encouraging 1-1 draw with Aberdeen at Pittodrie before the international break.
Ahead of their match against a side who have scored 15 goals in their last three domestic home games under new boss Ange Postecoglou, the Staggies manager told STV: "It is well documented how strong the start was going to be in terms of the teams and it is another challenge.
"Obviously it is one of the top teams in Scotland, playing them at Parkhead, with a new manager, a new group of players, they have been on a real good run recently.
"But I talk to my players, I show them evidence, I show them clips of the last couple of games and show them the belief they had against Rangers and show them the way they played against Aberdeen as well.
"A win anywhere is possible, it is making sure that you look at the challenge in front of you and the strength of the team in front of you.
"But at the same time you look to see where we can affect the game and have that belief going into it to make sure we give a really good account of ourselves."
Mackay was busy during the transfer window assembling a new-look squad and he is pleased with what he has seen so far.
The former Watford and Cardiff boss said: "There is a whole new group of players there.
"I think in the final count on deadline day it was 16 out and 12 in and for that 12 to join the group and gel is something that we have to do quickly.
"Obviously I am delighted with the way they are throwing themselves into it, the attitude they have and the culture that is growing, there is a work ethic about them that I like, an honesty I like.
"I have asked them to be selfless and the more they are, the more they will benefit from it."