Pulis reckons the former Newcastle and Crystal Palace boss is experienced enough to deal with the situation.
“I know Alan, he's got thick enough skin to cope with anything that's thrown at him," Pulis told Sky Sports.
“Arsene loses the Cup, nobody talks about him getting there, they talk about the performance and the defeat, so it's his turn to get criticism.
"It was Jose (Mourinho's) turn the week before. That's what the press do, that's what supporters do, if you're underperforming, you come under some stick."
Pulis added: "I left but I've got nothing but respect for the players and the group of people there, it's a wonderful football club."