"Sometimes in politics you get a wallop," Kenny told reporters.
Asked why he hadn't agreed to a TV debate, Kenny said he had wanted to avoid "a shouting match with political leaders."
Supporters of keeping the Senate argued the government now must strengthen the institution. They called for the Senate to gain the power to block legislation, not merely debate and on rare occasions delay it. Only the powerful lower house of parliament, the Dail, is directly elected and can reject government legislation.
"The moral pressure for reform is now absolutely overwhelming," said Dr. John Crown, an independent senator.
Any amendments to Ireland's 1937 constitution require majority voter support in referendums. The Irish have demonstrated a tendency to say "yes" to pollsters, but then vote no in private, with anti-government sentiment invariably higher than surveys suggest.
This time, unusually, both the conservative Fine Gael and most left-wing parties backed the idea of ending the Senate, with the nationalist Sinn Fein and hard-left socialists both decrying its air of privilege. Only the parties of the previous disgraced government, Fianna Fail and the Greens, opposed the measure.
Paul Murphy, an Irish Socialist Party member of European Parliament, said the result reflects "deep distrust of the government and shows that people have a desire to check and hold back the pro-austerity political establishment."
Kenny's government enjoys the biggest parliamentary majority in Irish history and doesn't have to face re-election until 2016. But it is publicly divided over the scope of the next austerity budget due to be published Oct. 15.