"But this stuff about being a pioneer - I'm not an American manager, I'm a football manager," the 58-year-old told reporters.
"There's not one person in Swansea who could care less about America, they care about this football club and that's why I'm here."
Bradley will be tasked with boosting the morale of the struggling Welsh side, who are fourth-bottom of the league table.
"We're a team that has had a little bit of bad luck and lost a bit of confidence," Bradley added.
"Sometimes when results go against you and you lose a bit of confidence, little things slip away from you a little bit. And now maybe there's moments when there's got to be a bit more confidence."
The former Egypt manager also added that his priority will be to re-establish the connection with fans, after certain sections expressed displeasure at the sacking of Guidolin.
"It's the number one thing. For a club to have any chance of being successful, you have to have connection with supporters and community, this is what it's about," he said.
"I have full respect for Franceso and I will do anything to earn their respect. But be clear about one thing, no matter what your name is, if you come to the league you have to earn respect."
Bradley also said that his sacking as the U.S. manager was a "mistake", and added that the England national side required a home-grown manager amidst British media reports linking current U.S. coach Juergen Klinsmann for the job.
"I don't appreciate the way it was done (fired as U.S. coach), I think they made a mistake," he added.
"I think there are times when it makes sense to go outside of the country to get a manager for the national team. But I think with England, you have to go inside."
(Reporting by Nivedita Shankar in Bengaluru, editing by Pritha Sarkar)
