He said Pakistan lost a "truly priceless opportunity" to strengthen its own security and its standing in the eyes of the world."
Mr. Clinton said he realizes Pakistan was responding to India's tests two weeks ago, but added, "Two wrongs don't make a right."
Earlier, Mr. Clinton's feelings were relayed by presidential spokesman Mike McCurry, who said the United States has strong, independent confirmation that Pakistan had followed the lead of archrival India in conducting nuclear tests.
CBS News White House Correspondent Bill Plante reports that President Clinton met Thursday morning with his national security adviser, Sandy Berger, to learn details. The officials say they don't have official confirmation there were tests, but they don't doubt the reports.
The United States considers the testing extremely serious because of the tension-filled history between Pakistan and India, Plante reports. This could be a flashpoint for possible nuclear war, and if nuclear weapons are detonated anywhere on the planet, it puts the United States and other nuclear powers in a difficult position, as well as killing whole populations and damaging the environment
Mr. Clinton had made a last-minute plea to Pakistan's prime minister, Nawaz Sharif, Wednesday night. McCurry said it was a "very intense," 25-minute call in which the president implored the prime minister not to conduct a test.
Asked whether Mr. Clinton felt snubbed by Sharif after the tests, McCurry said, "I think he well understands the difficulty of the situation the prime minister faced."
Nevertheless, the president pointed out to Sharif the consequences of testing, and said Pakistan would reap benefits if it refrained.
"The imposition of sanctions is a certainty under U.S. law," McCurry said. The United States cut off all nonhumanitarian aid to India after its tests and is trying to block all lending to India by the World Bank, International Monetary Fund and other international financial agencies.
McCurry said identical sanctions against Pakistan could be announced as early as Thursday.
In Pakistan, economic sanctions will mean a great deal more than they did in India, Plante reports, because Pakistan's economy is far weaker than India's.
After fighting three wars in the last 50 years, Pakistan and India are bitter rivals.
Mr. Clinton called Sharif shortly before midnight Wednesday amid signs that Pakistan was on the verge of testing. "He made that call, because we understood precisely the decision that the prime minister was wrestling with," McCurry said.
Sharif called the White House Thursday morning, presumably to notify Mr. Clinton of his deciion to test. By that time, the United States had independently confirmed what Pakistan had done.
Sharif did not initially reach President Clinton. "They may talk this morning, but the president has made clear that the imposition of sanctions is a certainty under U.S. law, and that the consequences that Pakistan will face will be real consequences because of the structure of our law and the requirements that are on us now in international financial institutions that we have to deal with," McCurry said.
U.S. intelligence officials said the tests were confirmed independently by seismic sensors and other methods.
A key final indicator that tests were imminent came from spy satellite images showing concrete-pouring equipment at a Pakistani nuclear test site, evidence that an explosive device was about to be sealed in a hole.
U.S. intelligence has been criticized for failing to provide advance warning of India's nuclear tests two weeks ago.