The Cherries boss has to choose a new skipper after Neto left on loan to Arsenal on transfer deadline day.
The Brazilian was their skipper, but is now set to be the no.2 for the Emirates Stadium club.
Iraola told the Daily Echo: “For me it's clear, I think that our captain is Adam Smith.
“He has experience, the leadership and he is going to be, he is already, a top captain.
“Lewis Cook also has the experience to be a captain, even with England in the youth teams, and they are very, very good.
“I don't want them to change anything, you know, they have to continue doing what they do.
“A lot of players, I think, can step up and even without the armband, they can be a support for the others.
“Probably I don't give the importance that here in England I feel you give to the one wearing the armband, because I think there are leaders that come naturally.
“But I'm happy that the first game he (Cook) takes the armband, he can score.
“(It was) probably not his best game, I told him, but he has been able to score a goal.”