Matt Connolly's header settled a tight game between the promotion hopefuls and gave City a record-equalling ninth straight win at the Cardiff City Stadium.
The result was all the more impressive given early injuries to Ben Turner and Andrew Taylor which forced Mackay to use teenagers Ben Nugent and Joe Ralls.
Mackay said: "I'm delighted with the character of the team and the fact we kept another clean sheet at home, but that is no surprise to me because I see that from the players every day.
"Middlesbrough had been on a roll and we knew it would be a tough game. But it became tougher when we lost two players after 20 minutes. We had to put young players in and they did brilliantly well.
"To show that resilience against a good team showed the commitment to the cause and there are no egos at this club."