"We are not shaken by a resolution from one place or another," said Arafat on Wednesday from his compound in the occupied West Bank city of Ram Allah.
"We are more important than any resolution."
US ambassador to the UN John Negroponte was the only member to veto on Tuesday the text calling on Israel to "desist from any act of deportation and cease any threat" to Arafat on grounds it did not condemn Palestinian resistance activities.
Palestinians, on their part, expressed concerns that Washington is turning its back on the "road map" aimed at ending the Palestinian-Israeli conflict.
US policy has become a "hostage" to Israel, said Palestinian cabinet minister Yasir Abd Rabbu.
Palestinian chief peace negotiator Saib Uraikat said the US move could be seen by Israeli leaders as a green light to assassinate Arafat.
"It's a black day for the United Nations and for international law," he said.
Israeli Prime Minister Ariel Sharon's government sparked international outcries after announcing it would "remove" Arafat. While it did not specify actions it would take, some Israelis suggested killing him.
US mediator "futile"
Palestinians have rallied daily
since Isreal threatened Arafat
"This is a clear announcement that the American administration is not willing to live up to its commitments under the road map," said Abd Rabbu.
"The American veto not only disappointed the Palestinian people and the Arab world but it shows that depending on the US efforts and US role is futile and useless," he said.
An advisor to Sharon, Dore Gold, accused Security Council members of ignoring what he said was violence against Israelis.
A war of words erupted between UN members within hours of the resolution - demanding Israel neither harm nor deport Arafat - being put to vote.
The resolution fell after America voted against the motion, while Britain, Bulgaria and Germany abstained leaving the remaining 11 members voting for.
The resolution was drafted by Palestinian UN envoy Nasir al-Kidwa and sponsored by Syria.
"Israel found itself in an Orwellian situation by which its war on terrorism was to be judged in a Security Council resolution sponsored by Syria, one of the main state supporters of terrorism in the world," Gold said.
But Syrian UN envoy Faisal Mikdad called the veto "regrettable" and said Israel "should not be a member of the United Nations because it is not a peace-loving country.
"Syria believes that Israel is responsible for its illogical policy and Israel is as well responsible for having scuttled the peace process in the Middle East," he said.
After the vote, Negroponte joined other council members in warning Israel the veto did not mean it should harm Arafat or send him into exile.
"Just to remind you that today is the 21st anniversary of the massacre of Sabra and Shatila. Do you remember that? Do you remember Mr. Sharon?"
Nasir al-Kidwa, Palestinian UN envoy
During nearly eight hours of harsh debate in the 15-nation Security Council on Monday, more than 40 governments condemned the decision to get rid of Arafat.
As he addressed the Security Council after the vote, al-Kidwa recalled the 1982 massacre of Palestinian refugees in Lebanon by Israeli-backed Lebanese militia.
The massacre took place while Israeli Prime Minister Ariel Sharon was defence minister. Sharon was later found indirectly responsible by an Israeli enquiry and sacked from his post.
"Just to remind you that today is the 21st anniversary of the massacre of Sabra and Shatila. Do you remember that? Do you remember Mr. Sharon?" al-Kidwa said.
Meanwhile, Israel's Finance Minister Benjamin Netanyahu said Israel should consider a truce made by a Palestinian security adviser.
Israel had earlier described Palestinian chief security adviser Jibril al-Rajub's proposal as a "honeytrap".