Former U.S. goalkeeper Tim Howard said on a podcast that the Bosnians were in for a brutal reality check at San Francisco Bay Area Stadium on Wednesday, while a network reporter mocked the nation on live TV before later apologising.
Barbarez said the hot takes were inevitable in the social media age and had no effect on the team.
"I have to admit things like that happen on a daily basis," he told reporters on Tuesday.
"We are a small country and sometimes things like that happen, but I have no problem with it.
"My boys don't have a problem with it ... You're playing for a place in the round of 16. If that's not motivation enough, then I don't really notice things like that."
Opposing coach Mauricio Pochettino was not embracing the co-hosts being favourites in his pre-match media conference but Barbarez had little doubt.
"Look, of course they are favourites. Their place in the rankings, they are the hosts, the names in their team - definitely," he said.
"We never had a problem with being the underdog. This role, this word, doesn't mean anything to me. You can throw this word around.
"It's important what happens on the pitch, and this is what I'm interested in. This is what we are interested in."
Bosnia's players compete in leagues all over the world, including U.S.-born attacker Esmir Bajraktarević, who Barbarez said had brought a unique perspective to the team.
"Those touches of American culture are also very important because we have guys who were born all over the world," he said.
"Maybe that's a big advantage for us - that we've managed to bring together all those cultures, habits, mentalities and different approaches to football into one unit."