Striker Chamakh was through on goal midway through the first half of Palace's 2-0 defeat but appeared to dive in an attempt to win a penalty despite being well placed to score.
The Moroccan was promptly shown a yellow card and then exchanged words with left-back Moxey.
The argument continued as they walked off the pitch at half-time, through the tunnel and into the dressing room.
Boss Ian Holloway did not fine Chamakh for the dive but revealed: "He got the hairdryer."
Holloway added: "I don't think I can repeat what I said at half-time, but I nearly took my jacket off to both of them.
"You have to deal with things. I've since called them in and showed them the incident and asked what it was about. It was amicable in the end but passions flare up when you are not winning.
"The passion was there and I think it shook everybody. It rocked this club, we are built on that togetherness.
"But I've watched the incident and spoken to Chamakh and his explanation is actually quite good.
"He headed it and was just looking at the ball, and he said if he'd been at Arsenal he would have got a penalty.
"But I still think he should have shot."