Former Cardiff midfielder Aaron Ramsey opened the scoring with a header in the 29th minute, before delivering the final blow in second-half stoppage time after substitute Mathieu Flamini had made it 2-0 four minutes from time.
The hosts pushed for an equaliser after the break with the score at 1-0, leading to a much more open game, but Mackay has no regrets over the change of approach that allowed Arsenal the space to extend their lead.
"We were obviously playing against a very good team today," he said. "But I'm very proud of the team that I've got myself because we tactically made sure that we kept the ball in front of us in the first half.
"We limited them to few chances in that first half and then second half decided to press a little bit higher when space opened up.
"I don't apologise for going for it a little bit then because we're 1-0 down and we have to try and break their back line and upset them and stop them from keeping the ball for the rest of the game.
"We had to go for it. I was very proud of the bravery and the way they did that.
"I'd rather lose three and have a real go, and that's what we did. We made sure that we gave them some problems throughout the second half.
"We're playing against the best, and we're certainly not out of our league."
Ramsey was treated to a standing ovation from all four sides of the Cardiff City Stadium after the final whistle, and Mackay was quick to praise the club's fans and the in-form midfielder.
"They're a class act," he added. "They're very passionate football people. He was one of their own, and there's plenty of grounds that people get booed at for that.
"I know the young man and he's also a class act. Our fans today showed their appreciation."
