Khamenei spoke one day in Tehran after the United States restored sanctions on the Islamic State's shipping, energy and financial sectors and on the eve of the anniversary of the 1979 takeover of the U.S. embassy in Tehran.
Trump "has disgraced the remnant of America's prestige and that of liberal democracy. America's hard power, that is to say, their economic and military power, is declining, too," Khamenei said Saturday on Twitter, quoting a speech he gave earlier in Tehran.
Khamenei addressed thousands of students one day before the takeover anniversary, which is marked every year with nationwide rallies.
"The challenge between the U.S. and Iran has lasted for 40 years so far and the U.S. has made various efforts against us: military, economic and media warfare," he said. "There's a key fact here: in this 40-year challenge, the defeated is the U.S. and the victorious is the Islamic Republic."
The U.S. sanctions take effect Monday.
Earlier, Trump re-imposed other sanctions on Iran after withdrawing from the 2015 nuclear deal in May.
"America's goal with sanctions is to cripple and hold back Iran's economy, but the outcome is that the push toward self-sufficiency has expanded in the country," Khamenei said in his speech. "Over the years, the Iranian nation had become accustomed to importing everything, but now it is accustomed to seeking to produce everything."
Khamenei said under Trump "every decision is faced with opposition not only from people but even governments around the world."
Trump wants to negotiate a new deal with Iran to replace the agreement also reached with China, France, Russia, Britain, Germany and the European Union. Sanctions were lifted in exchange for Tehran reducing its stockpile of enriched uranium and allow the International Atomic Energy Agency to regularly inspect nuclear facilities.
"These sanctions hit at core areas of Iran's economy," Secretary of State Mike Pompeo announced Friday. "They're necessary to spur changes we seek on the part of the regime. In order to maximize the effect of the president's pressure campaign, we have worked closely with other countries to cut off Iranian oil exports as much as possible."
He said the U.S. government will issue temporary exemptions for eight undisclosed countries who import crude oil from Iran because they "made important moves" to reduce the imports.
Iran has said the European Union, Russia, China supported the Islamic Republic and denounce the sanctions.
Sunday has been designated as Student Day in Iran.
"Our youths all over the country have pro-independence feelings; some of them do not even have a very religious commitment, but they are sensitive to foreign domination," Khamenei said. "Of course, the United States sees some of these things down to us and threatens us, saying 'If the youth of such and such neighboring country attack our forces, we will hold you culpable'.
"Well, you're dead wrong to blame us! People in Iraq, Syria, Lebanon, Afghanistan and Pakistan hate you. What does this have to do with us?"