Lord Neuberger has ripped into the British press for its coverage of Article 50
Lord Neuberger also claimed politicians could have been "quicker and clearer" in defending the judiciary after the High Court ruling that Theresa May did not have the power to start the Brexit process without the consent of Parliament.
The High Court's ruling led to sharp criticism of the three judges involved from Eurosceptic newspapers, and Lord Chancellor Liz Truss came under fire for failing to speak out quickly enough to defend them.
Lord Neuberger and his colleagues at the Supreme Court rejected a Government appeal against the ruling last month.
Lord Neuberger did not single out any politicians or newspapers, but told the BBC: "We were certainly not well treated.
"One has to be careful about being critical of the press, particularly as a lawyer or judge, because our view of life is very different from that of the media.
"I think some of what was said was undermining the rule of law."
Liz Truss has been criticised for not being quick enough to stand up for the High Court judges
Asked whether politicians responded quickly enough to defend the judiciary and rule of law, Lord Neuberger told Radio 4's Today programme: "They were certainly vocal enough quickly enough after our hearing.
I think some of what was said was undermining the rule of law
"After the [High] Court hearing, I think they could have been quicker and clearer. But we all learn by experience, whether politicians or judges. It's easy to be critical after the event.
"They were faced with an unexpected situation from which, like all sensible people, they learned."
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Lord Neuberger said undermining the judiciary also undermined the rule of law as judges were "the ultimate guardians" of it.
The Supreme Court president argued that Eurosceptic newspapers have 'undermined the rule of law'
Government Loses Brexit Vote Appeal
Tue, January 24, 2017
Britain's most senior judges ruled that Prime Minister Theresa May does not have the power to trigger the formal process Article 50 for the UK's exit from the European Union without Parliament having a say.
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Issued by the Supreme Court of (top row, from the left) Lord Neuberger, Lord Mance, Lord Kerr, Lord Sumption, (bottom row, from the left) Lady Hale, Lord Clarke, Lord Wilson and Lord Hodge, who agreed with the majority decision that the Government could not trigger Article 50 without Parliamentary approval.
"The rule of law together with democracy is one of the two pillars on which our society is based," he said.
"And therefore if, without good reason, the media or anyone else undermines the judiciary, that risks undermining our society.
"The press and the media generally have a positive duty to keep an eye on things. But I think with that with that power comes the degree of responsibility."
Lord Neuberger, who is due to retire later this year, was speaking as the process was launched to appoint new judges to the Supreme Court, including his successor as president.