The Bluebirds were second best for much of the game with Norwich ending up with 31 shots on goal.
Cardiff held firm though, and Mackay was pleased with David Marshall after his part in Chelsea's goal last weekend.
"I'm delighted with the team defended," Mackay told Sky Sports.
"Overall [Marshall] was disappointed with his performance last week. He did what he had to do today. He's been magnificent for me for two-and-a-half years."
The result meant that Cardiff remain a point ahead of Norwich in the Premier League.