Between 13 and 15 tonnes spilled into the sea from the Brent Bravo, 116 miles north east of Lerwick, in May 2013.
Senior management from Shell were at Aberdeen Sheriff Court where the company admitted the release of fuel.
Sheriff Kenneth Stewart fined the company Â£6,650, reduced from the maximum possible due to the early stage of the guilty plea.
A Shell UK spokeswoman said: "We regret that the release occurred - no spill is acceptable.
"We have since carried out a thorough investigation into the incident and have shared the lessons learned across the business."

Pedro Godinho, 22, died in hospital after being discovered in Canonsleigh Road, Leicester, on Sunday morning.
Ezekiel Braithwaite, of no fixed address, has been charged with murder and attempted grievous bodily harm.
Taome Stabanner, 21, of Rowena Court, Mountsorrel, has been charged with assisting an offender.
Both are due to appear at Leicester Magistrates' Court later.
Mr Godinho's cousin, Rafael Godinho, said on behalf of the family: "Pedro was sadly taken from us. He was only 22-years-old, with a promising life ahead of him.
"At this time, the family is working closely with Leicestershire Police.
"Anybody who knows him would tell you what a good heart he had, he'd be the one to give you the shirt off his back."
Oil giant Shell has been fined thousands of pounds after a diesel leak on board a North Sea platform.
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A 19-year-old man has been charged with murder after another man was found fatally stabbed after an attack in a residential car park.