The Flying Phantom sank in December 2007 while towing a cargo vessel in poor visibility on the River Clyde near Clydebank.
At the High Court in Glasgow yesterday, tug company Svitzer Marine Limited pleaded guilty to a series of health and safety breaches.
The Danish firm failed to act following a previous incident involving the same tug in December 2000, the court heard.
Peter Gray QC, acting for Svitzer, said. "Ever since December 19 2007, it has been a matter of the greatest regret that, in relation to the towing in restricted visibility, the firm failed to meet the very high standards it sets itself.".
Stephen Humphreys, 33, from Greenock, Eric Blackley, 57, from Gourock, and Bob Cameron, 65, from Houston, Renfrewshire, died when the tug was overtaken by the vessel it was towing, the Red Jasmine, and capsized.
A fourth man, Brian Aitchison, 37, from Coldingham in the Borders, managed to swim free and was rescued.
Lord Turnbull will sentence Svitzer, whose UK office is in Middlesbrough, next month.
On December 29 2000 the Greenock-based Flying Phantom suffered £150,000-worth of damage when it was hit by a vessel it was towing on the Clyde, the court heard.
Dense fog saw the tug run aground and then struck by the ship in the same stretch of river as the 2007 sinking.
Prosecutors said the tug firm, formerly known as Wijsmuller Marine Ltd, was aware of the hazards associated with towing in dark, foggy conditions in the Clyde.
But in the aftermath, no plans were made for disconnecting tugs in conditions of reduced visibility.
The court heard details of the night The Flying Phantom sank.
Advocate depute Alex Prentice said the last radio contact with the tug was made just before 6pm, when the crew told the Red Jasmine pilot: "We're stuck on the bank."
He said the pilot replied: "Let go the line then, please"; to which the Flying Phantom responded: "Will do."
Mr Aitchison told investigators that he and Mr Humphreys were in the wheelhouse and the others below when the tug lurched to one side.
The survivor pressed the tow release button but "the winch appears not to have released the towline quickly enough", Mr Prentice said.
Port operator Clydeport Operations Limited is also being prosecuted over the incident. A hearing will take place in Edinburgh in December.