The US technology giant told the Court of Appeal in London it would need two weeks to replace the current notice - which Samsung said did not comply with a court order.
But Lord Justice Longmore said he was "amazed" it would take Apple such a long time to publish the statement.
"We are just amazed that you cannot put the right notice up at the same time as you take the other one down," he said.
Sir Robin Jacob added: "I would like to see the head of Apple make an affidavit about why that is such a technical difficulty for the Apple company.
"I don't believe the instructions you have been given.
"This is Apple that cannot put something on their own website?"
The judges ordered the company to re-post the notice within 48 hours.
The court was hearing the latest stage of a long-running legal dispute over the firms' tablet computers.
Apple claimed Samsung's Galaxy Tab infringed its copyright - but the Court of Appeal upheld the original ruling that it was not "cool" enough to be confused with the iPad.
In October, the two judges agreed with the decision that the Samsung Galaxy tablets did not infringe Apple's registered design.
Following the appeal, Apple was ordered to publish details of the judgement on its website, and place prominent adverts in several UK newspapers and magazines.
The lawyer representing Apple, Michael Beloff QC, told judges the company thought the statement on its website had complied with the court order.
"It's not designed to punish, it's not designed to make us grovel, " he said.
"The only purpose must be to dispel commercial uncertainty."
But the judges decided in favour of the South Korean company, telling Apple to make the required changes.
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