The Bluebirds ended a 51-year absence from the top flight, after three successive near misses in the Championship play-offs.
And the result came 53 years to the day since a home win over Aston Villa saw the Bluebirds last promoted from the second tier.
Mackay said: "It's been a long time coming and we're here now. I'm delighted.
"It's not sunk in, there's a lot of smiley happy faces and it's going to be a long night in Cardiff.
"It's something we'll reflect on over the next few days but there's been a lot of hard work from a lot of people at the club and I'm delighted for these people.
"They have backed me and the team in the last 18 months and for that I'll be forever grateful. I hope this goes a little way to repaying the backing they have given me since I came in."
Since being relegated to the old Division Three in 2001 Cardiff have withstood two changes of ownership, financial difficulties and winding up orders.
And Mackay, who took charge of the Welsh side in 2011, believes such troubles can finally be put behind them.
"There's a lot of people here that have gone through a lot of hard times. This is for them," he said.
"The staff at the football club, back office and the training ground staff, directors, people who have worked here over the last couple of years, players and fans and the people of Cardiff. It's a night for them."
Mackay added: "We have been competitive in this league, every team we have played in the last 20 months we have been competitive against. That will not change in the Premier League."
Cardiff forward Craig Bellamy called for the club to top the season by going up as champions.
"We wanted to get the game won and get it over with," he said.
"It's just nice to get over the finish line. We can see where we go in the next couple of weeks and finish it off properly as champions."