"We have no judgement on this election because America is the same America," he told thousands of people during a public speech in Tehran, broadcast on state television.
"In the past 37 years, neither of the two parties who were in charge did us any good and their evil has always been directed toward us."
It was his first reaction to the election of Trump, who during his campaign labelled last year's nuclear deal between Iran and world powers a "disaster" and threatened to tear it up.
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"We neither mourn nor celebrate, because it makes no difference to us," Khamenei said.
"We have no concerns. Thank God, we are prepared to confront any possible incident."
Khamenei pointed to several bitter encounters with different US administrations, including the 1988 shooting down of an Iran Air passenger jet by the USS Vincennes that killed 290 people.
Tehran and Washington have not had formal diplomatic ties since 1980, when Islamist students stormed the US embassy and held staff hostage for 444 days.
Opposition to the US has remained a central plank of Iran's foreign policy, despite last year's nuclear deal.