Loic Remy struck twice in the first half to give Alan Pardew's men a commanding half-time lead, while the home side were unable to capitalise on Peter Odemwingie's strike after the restart to find an equaliser.
The loss was Cardiff's second in a row at home and Mackay was annoyed with his side's inability to get out of the blocks as they dropped to 12th in the Premier League table.
|5/2||Cardiff are 5/2 with bet365 to be relegated
"Second half, I thought we were what Cardiff City is about and we were excellent. On another day we could have come back and got a point out of it, but you cannot start like that.
"This has maybe happened three or four times in two and a half years, in terms of the way we started and the way that the whole group, in the first half, were half a yard off the pace. But, to be fair, in the second half the whole group were absolutely on the pace.
"Sometimes, that just happens, but it's something we need to make sure happens as few times as possible, because you're immediately punished in this league by very good players."
Mackay was quick to reject claims that the introduction of Jordon Mutch was solely responsible for his side's improved performance after the break.
"He certainly came on and made a difference, but I would suggest that everyone upped their game and were back to being the players I know that I've got here," Mackay continued.
"I think we were playing against a good team here and some very good individual players, so we had full respect for the team that we were coming to play against and we knew it was going to be a tough game."