The Reds snatched a 2-1 win at Selhurst Park in controversial fashion as Christian Benteke scored from the spot deep into injury time after Damien Delaney was deemed to have brought him down in the box.
Referee Andre Marriner had appeared unsure whether to point to the spot but did so after one of his assistants, Scott Ledger, flagged.
And, speaking on the Alan Brazil Sports Breakfast, Halsey said Pardew had every right to feel aggrieved.
“I am at Manchester City’s training complex and we have got a group of American referees over doing an international development course and all to one said it is not a penalty, he has gone down far too early,” he said.
“Contact doesn’t mean to say it is always going to be a free-kick or a penalty. Personally, I think Benteke has gone down far too easily.
“Looking back at it, I think Andre will be a bit disappointed that they have given a penalty.
“I believe Benteke has gone down far too easily and Andre should have been shouting down the headset [at his assistant referee], ‘not for me, not for me, no pen’.”