The Conservative government has said it will appeal Thursday's court decision and May told EU leaders on Friday that she believes she has a strong case.
But in a statement published ahead of a trade mission to India, May cautioned members of parliament against using the ruling to undermine the result of the June referendum.
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"The result was clear. It was legitimate. MPs and peers who regret the referendum result need to accept what the people decided," she said.
Supporters of Brexit responded angrily to the court's decision, amid speculation that pro-European lawmakers would seek to water down the break with the EU and derail May's plans to begin formal exit talks by the end of March.
"Now we need to turn our minds to how we get the best outcome for our country," the prime minister said.
"That means sticking to our plan and timetable, getting on with the work of developing our negotiating strategy and not putting all our cards on the table. That is not in our national interest and it won't help us get the best deal for Britain,” he added.
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The High Court ruled that the government does not have the power to trigger Article 50 of the EU's Lisbon Treaty, which would set off a two-year countdown to leaving the bloc, without the prior approval of parliament.
Opposition labour leader, Jeremy Corbyn has said that he will not seek to reverse the referendum result.
But he told the Sunday Mirror tabloid that he would vote against Article 50 unless May agreed to press for continued access to the European single market and guarantee EU workplace rights after Brexit.
"These must be the basis of the negotiations. And it doesn't necessarily cause a delay," he said.
Corbyn added, "We are not challenging the referendum. We are not calling for a second referendum. We're calling for market access for British industry to Europe."
The High 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.
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