Wren Sylvia Panter and Petty Officer Ian Luff - both married - spent more than pounds 2,000 of the money on the Greek island of Corfu.
But nine days after leaving the aircraft carrier in September last year, they gave themselves up in Barcelona, Spain.
Panter, 27, of Camberley, Surrey, and Luff, 30, of Sandown, on the Isle of Wight, admitted going absent without leave and misapplication of ships funds. They both denied theft and desertion.
The court was told they considered the money to be a 'loan' and intended to pay it back by selling their story for pounds 10,000 to the Sun newspaper.
Lieutenant Commander David Steele, for the prosecution, told the hearing at Portsmouth that Panter had used her key to the safe in the wardroom accounts office, where she worked, to take the pounds 11,301 in British and Greek currency.
She had been upset on the day they left the carrier, anchored off Corfu, because her shore leave had been cancelled.
When they turned up in Barcelona they handed over the equivalent of pounds 9,160, having spent pounds 2,141, Lt Cdr Steele said.
The court was told that Panter had been warned about her affair with Luff by her superior officers. She was told if it continued she might be removed from the ship.
'Her belief was that it was none of the Navy's business. She said if the Navy did return her to the UK, she would go to the newspapers,' Lt Parton said. Superior officers considered the behaviour of Panter to be 'emotional' and unseemly.
But a colleague, leading steward Steve Pleasance, told the court that Panter was unhappy on the ship - it was her first time at sea - and she was feeling the strain. 'She was very, very confused,' he said.
The hearing resumes today.