Alvaro Negredo pulled one back in the second of six minutes of added time, triggering flashbacks for Mackay of the way Manchester City had scored twice in stoppage time to win the title on the final day of the 2011/12 season.
"They do not lie down and I had visions of Sergio Aguero scoring against QPR in the last game of the season a couple of years ago in injury time," the Cardiff manager said after his team's first ever Premier League home match.
"You want to play against the best in the best league in the world and we are doing that and I am proud of everyone at the club. There have been lots of downs but everyone here will have a smile on their face tonight."
It was The Bluebirds' first top-flight victory since 1962 with Cardiff having lost their Premier League opener at West Ham United last weekend.
"We deserve to be here. We have a great record at home," Mackay said. "Everyone realises how difficult it is to win away from home. We have to make sure Cardiff is the same sort of fortress it was in the Championship last season."
The South Wales club, who won the second division comfortably last term, have seen plenty of change since they were last in English soccer's top tier.
Now under the ownership of Malaysian billionaire Vincent Tan, they have changed their club colours from blue to red, and spent heavily since sealing promotion to try to ensure their stay in the Premier League lasts more than a single season.
Mackay said this win was just rewards for the support shown to the club in a part of the country where they must compete with rugby for attention.
"The atmosphere was fantastic before the game and to go and give a performance like that against a team like that was amazing," he said.
"We have to believe we can compete. The team were incredibly disciplined and as the game grew, we grew. We knew we had the ability to counter them but they are a very good team and if we didn't do our job properly they would punish us."
Former Manchester United striker Campbell has had a somewhat nomadic career, having had loan spells at Royal Antwerp, Tottenham Hotspur and Hull City as well as spending four seasons at Sunderland before joining Cardiff in January.
With Andreas Cornelius, an 8 million pound ($12.47 million) signing from FC Copenhagen sitting on the bench, Campbell took his opportunity with two headed goals from corners and a bright effort around the pitch.
"They had a centre midfielder playing centre back, so you knew there'd be a bit of an opportunity there," Campbell said, referring to City's decision to bring in Javi Garcia alongside Joleon Lescott in the absence of injured Vincent Kompany.
"There was some great deliveries into the penalty box, and it was a great team performance."
($1 = 0.6413 British pounds)
(Reporting by Josh Reich; Editing by Sonia Oxley)
