Mackay saw his team fall to their third defeat in five and Cardiff now have just one win in their last nine league matches.
Cameron Jerome put the hosts ahead at Selhurst Park in the sixth minute against his former club, just four minutes after Fraizer Campbell had missed an excellent headed chance to give Cardiff the lead.
Marouane Chamakh doubled Palace's advantage in the 57th minute to seal a third win in four for Tony Pulis' side, leaving Mackay to bemoan his side's finishing.
"In the first five minutes we should have scored and that changes games," he said.
"We certainly weren't at it the way we have been but even then it's about taking chances.
"We've got to be better at our end, they (the players) are all disappointed we've been beaten, and if we get chances we've got to take them."
Cardiff's slump in form has seen the Welsh side slip down the table to just above the relegation places.
Mackay added: "We knew it was going to be a tough game," he said.
"There's a big crowd right on top of the pitch and a new manager and that impetus and the battling qualities that we know were going to come with that.
"None of that surprised us obviously but it was one of those days that you know you're going to be up against it and you've got to match that.
"It's about keeping picking up points which we know is not easy to do in the Premier League.
"As far as I'm concerned it's about performances and obviously picking up points as we go."
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