Mrs May's speech to the National Conservative Convention in Oxford on Saturday evening came as MPs prepare for a series of votes on Wednesday which could see Parliament take control of the Brexit process.
Delegates at the convention overwhelmingly backed a symbolic motion saying Brexit should not be delayed, and leaving without an agreement should remain an option.
Mr Clark, the business secretary, along with Ms Rudd, the work and pensions secretary, and the justice secretary, Mr Gauke, had earlier said they would be prepared to defy Mrs May and vote for a delay to Brexit.
They argued there "simply will not be time to agree a deal and complete all the necessary legislation" unless a deal is approved in the coming days.
An amendment tabled by former Tory minister Sir Oliver Letwin and Labour's Yvette Cooper would give Parliament the opportunity to delay Brexit and prevent a no-deal situation if there is no agreement with the EU by the middle of March.
But Mrs May told activists: "Our focus to deliver Brexit must be absolute.
"We must not, and I will not, frustrate what was the largest democratic exercise in this country's history. In the very final stages of this process, the worst thing we could do is lose our focus."
Mrs May also said there should be no moves to deselect MPs because of their views on Brexit.
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