Truss had been criticised for staying silent over the backlash against Thursday's landmark judgment that the government cannot start the process of leaving the European Union without parliament's approval.
One newspaper denounced the three judges as "enemies of the people" while members of Prime Minister Theresa May's Conservative party accused them of "judicial activism" and of seeking to undermine the June referendum vote for Brexit.
"The independence of the judiciary is the foundation upon which our rule of law is built and our judiciary is rightly respected the world over for its independence and impartiality," Truss said in a brief statement.
Just a few hours earlier, the Bar Council, which represents barristers in England and Wales, had issued a statement of regret at the minister's silence over "serious and unjustified attacks on the judiciary".
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As justice minister and Lord Chancellor, Truss took an oath to defend the independence of the judiciary.
"A strong independent judiciary is essential to a functioning democracy and to upholding the rule of law," the council said in a statement.
The ruling prompted outrage among supporters of Brexit, sparking fears that it could delay the process that May had promised to start by the end of March.
Before the ruling, the prime minister had condemned those who brought the legal challenge, saying they were trying to "subvert" democracy.
The court decision has fuelled speculation that May might call an early election to strengthen her support in the House of Commons before the EU vote.
The next election is not due until 2020, but The Daily Telegraph newspaper reported that ministers were now discussing the option of bringing the date forward.
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