Fraizer Campbell was the hero for Cardiff with two late headers to earn the home side the three points after Aron Gunnarsson cancelled out Edin Dzeko's opener.
Alvaro Negredo's late strike set up a tense finale, but Cardiff held on to record a memorable victory and Mackay felt his side deserved the win.
"They were fantastic to a man, disciplined, did their job today and deservedly won the game," Mackay told Sky Sports 1HD.
Mackay also had special words of praise for Campbell for scoring twice with headers from corners.
"I think he gave Javi Garcia a very tough time during the game," added Mackay.
"We worked hard on our set-pieces and we have got good players in there that can aggressively attack the ball as long as the ball comes in with quality and Fraizer's like that
"We had good movement and fantastic crosses coming in and that is something that is difficult to defend for anyone."
Mackay was happy with his side's discipline as they dealt with whole occasion as Cardiff City welcomed back top flight football for the first time in 51 years.
"It's about being professional and not being caught up because we've got a fantastic crowd here. And for the first time in our history we're in the Premier League playing against a team who we go a goal down against and they only lost one game last year from being a goal down and they've got a tremendous clean-sheet record and we knew that it was going to be tough at that point, but we remained disciplined, organised and I felt there was a lot of belief in our ability today."
"I knew that they were never going to let their guard down and go to the last minute.
"We were playing against top, top players. I've spoken to the boys about how proud they should be because they deserve to be here and they deserve to be out there playing against these top players and it is about belief and believing in your own ability
"I thought tactically the players out there did an incredible job today and deservedly won the game."