He vowed to change the law "as quickly as possible" to allow the right to anonymity to be restored.
Ms Smith said the government was seeking agreement with the Tories on the best way to proceed.
This could include legislation, she said, but she declined to say whether she believed an emergency bill would be necessary.
She said: "I certainly accept, and I said some time ago, that there is a problem here that we need to solve. We are working now... to look at what we need to do to put this right."
Following Tuesday's development, a Ministry of Justice spokeswoman said: "We are studying the judgment carefully and urgently considering its implications, including amending statutory law."
Judge Paget said it would be "frankly impossible" to ask the jury to forget what they had heard from anonymous witnesses.
He told the jury: "You have heard evidence from a number of witnesses that you should not have heard."
He said the Law Lords had given their ruling "because of the difficulties caused to the defence if they do not know the identity of witnesses against them and are deprived of investigating why these people may be inaccurate or, worst, untruthful".
Ravi Sukul, a defence lawyer in the case, welcomed the judge's decision, saying that anonymity had created "a serious disadvantage" for defendants.
"They were never in a position to investigate the character of those witnesses to establish, for example, whether they are credible witnesses, whether their evidence ought to be believed," he said.
"The bottom line is, in my opinion, that fairness has prevailed."
Reaction from Ken Jones to the witness ruling
The BBC's Danny Shaw said there were a number of other cases in progress around the country that could be affected by the ruling, including one in Newcastle.
He added that as the ruling also affected convictions, it could prompt some defence lawyers to consider an appeal.
Several recent, high-profile trials have also used anonymous witness testimony, including those following the murders of schoolboy Michael Dosunmu and care worker Magda Pniewska.
The solicitor for two of the four men found guilty of murdering Birmingham teenagers Charlene Ellis and Letisha Shakespeare in 2003 has said they will appeal.
Errol Robinson told the BBC his clients' convictions had relied heavily on a key anonymous witness with "a very questionable background".
But Bob Quick, head of Scotland Yard's Counter Terrorism Command, said the ruling was "catastrophic".
"There is too much principle and not enough pragmatism in the criminal justice system," he said.
The Met's specialist Trident squad has encouraged witnesses to come forward to help prosecute gun crime on the assurance that they could remain completely anonymous.
Businessman Charles Butler was murdered in east London in 2004
Ken Jones, president of the Association of Chief Police Officers (Acpo), told the BBC that some "emergency legislation" was needed.
"There are about another 40 cases in the pipeline and a number of appeals are pending," he said.
"It's fundamentally important that we are able to protect, in very, very rare cases, anonymity of witnesses, otherwise we're not able to get justice for people."
Shadow Justice Secretary Nick Herbert said the Tories shared police concerns about the Law Lords' ruling.
He said: "The public must be protected from the most violent criminals. We are already discussing these issues constructively with the government to consider what legislation may be necessary."
Liberal Democrat justice spokesman David Howarth said: "Intimidation of witnesses is a very serious problem, but a balance must be found which protects them without compromising the integrity of the trial."
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