Former United striker Fraizer Campbell led the line impressively and netted an equaliser for the hosts after Wayne Rooney gave United a 15th-minute lead.
Patrice Evra headed home Rooney's corner on the stroke of the interval but Cardiff got the result they deserved at the death to edge three points clear of the Premier League relegation zone when Kim Bo-Kyung converted Peter Whittingham’s stoppage-time free-kick.
"I was delighted with our performance," said Mackay. "I think our first-half performance was possibly one of our most complete performances of the season so far, in the way we played and also (having) the belief to play against a team like Manchester United – the champions – and go and play like that.
"So I'm delighted with the performance from the first minute to the last.
"It probably felt like a defeat when they scored in the last minute of the first half. I was really disappointed with that for the team because of the way we played.
"But second half, the goal at the end was thoroughly deserving of the performance overall and the chances we had."
Cardiff maintained an impressive high tempo throughout, recalling their excellent early season victory over Manchester City, and Mackay was keen to underline that craft and guile sits alongside blood and sweat in his team's armoury.
"There's just a work ethic that we have at the club – in terms of training and in terms of playing," he said.
"I want the players who have a huge work ethic at the football club but they have to have technique and they have to have talent.
"I take the work ethic as a given. What I loved more about the team today and the way we've played this season is the belief they’ve show in their ability to play at this level and work their way up the pitch with the ball.
"That's the confidence that they're showing to compete at this level and compete well."
