The Bluebirds secured one of the most famous victories in the club's history with a stunning 3-2 win over Manchester City in their first top-flight home game in 51 years.
Having fallen behind to Edin Dzeko's superb strike, a close-range Aron Gunnarsson effort and a brace of headers from corners by Fraizer Campbell ensured Alvaro Negredo's late strike was not enough for the 2011-12 Premier League champions.
While Mackay has strengthened the Cardiff squad with the addition of club-record signing Gary Medel, Steven Caulker, Andreas Cornelius and John Brayford, it is largely the same group which secured the Championship title last term.
Some had questioned whether the Scot had enough quality at his disposal to avoid a rapid return to the second tier, but the starting XI that faced Manuel Pellegrini's side included nine regulars from last term.
Mackay said: "I spoke to the players about the fact that they have to believe they belong here. We were undoubtedly playing against one of the top teams in Britain and Europe and a team filled with top, top talent.
"But you want to test yourself against the best. I want to test myself against the best managers, and my players should want to test themselves against the best players in the world and be in the best league in the world.
"They are here on merit, they won the Championship last year and they were out there against City and you saw the belief.
"I have got technically very gifted players, and when we got the ball back we could counter-attack and hurt a team who are a top side.
"The best have come here and we deserved to beat them. That should give the players confidence we are here to compete every week and make sure it will be difficult for opposition to play against us."
Mackay also praised the tireless performance of goalscorer Gunnarsson who, alongside Medel, did much to stymie City's effectiveness in midfield.
The Iceland international's pre-season preparations were hindered after he dislocated his shoulder on international duty, but he showed no ill-effects as he constantly hassled and harried.
"Aron became captain of Iceland when he was just 23, but he is a player who just goes quietly under the radar," said Mackay.
"As last season went on he became more and more important to our team.
"I think it was about him growing up as a player over the last two years and he has done that.
"He has become a more mature player and with an experienced player in Gary Medel alongside him, he showed that maturity against top players."
For Pellegrini the defeat was a rude awakening after the ease with which City brushed Newcastle aside in his first game in charge.
The Chilean admitted defensive mistakes had cost his side, but tried to remain positive when it came to City's play at the other end of the pitch with Dzeko and Negredo getting on the scoresheet.
"It is always important to score, Edin played well and Alvaro is a very important striker for us also and he scored when he replaced him," he said.
"That shows we are strong as an attacking team and it is always good to score two goals away from home, it is just we had other problems."
Poor defending played a part in all three Cardiff goals as City struggled without the influence of injured captain Vincent Kompany, but Pellegrini does not believe the performance shows he must add to his defensive options.
He said: "I do not like to link the two things, it is not the same thing. We did not lose the match because we do not have any centre-halves, we lost because we did not concentrate at two corners. It is something we will work on during the week."