Stephen Humphreys, 33, Eric Blackley, 57, and Robert Cameron, 65, died when the Flying Phantom capsized in thick fog in the River Clyde in December 2007.
At the High Court in Glasgow yesterday, tug company Svitzer Marine Limited pleaded guilty to a series of health and safety breaches.
It admitted failing to put in place a safe operating procedure after a previous grounding in December 2000. The tug that time had been towing the Egyptian Abu Eglia cargo vessel.
Thompsons Solicitors, which acts for the families, said the length of time the case had taken to get to court had prolonged the grieving process.
Despite requests from the widows of the men a fatal accident inquiry has never been granted.
Andrew Henderson, a partner at Thompsons, said: "The guilty plea is to be welcomed but we must not forget that the families of the deceased have waited an unnecessarily long time for this to come to court.
"The widows and families of the deceased have been failed by a system which has prolonged their grieving process by failing to hold a fatal accident inquiry (FAI) to establish a clear picture of the events leading up to their loved ones deaths on that fateful night.
"There has been an inability to learn lessons from the accident and prevent future tragedies due to a lack of FAI almost six years on from the deaths. While Svitzer's guilty plea will provide some comfort it remains to be seen what the High Court will deem a sufficient punishment."
Pat Rafferty, Scottish secretary for the Unite union, said the families of the deceased had been "let down by an FAI system which is little more than a lottery as to whether tragedies like the Flying Phantom will be investigated".
He added: "Unite has been calling on the Scottish Government to fast track legislation which will radically overhaul and improve the system. This simply serves to reinforce these calls not only for an FAI to determine exactly what happened but to ensure we have a robust and fit of purpose system for the future."
Svitzer's QC Peter Gray said what happened was an appalling tragedy and that the company's remorse was deep and genuine.
A judge will now decide next month what fine the firm will face.
The Flying Phantom, which was based at Greenock, was trying to guide a cargo vessel to a dock when it sank opposite Clydebank College in West Dunbartonshire on December 19, 2007.
Crewman Brian Aitchison, from Coldingham, was rescued from the water after he managed to escape from the tug's wheelhouse.
The bodies of skipper Mr Humphreys, from Greenock in Inverclyde, along with Mr Cameron, from Houston in Renfrewshire, and Mr Blackley, from Gourock, Inverclyde, were later recovered. The tug itself was raised in a salvage operation the following month.
Prosecutor Alex Prentice, QC, said visibility had "significantly diminished".
The court heard how there had been radio contact with the Flying Phantom until it suddenly ended.
Mr Prentice added Svitzer took no suitable steps to implement control measures identified after the Abu Eglia incident.
He also told the court that had Svitzer been more proactive about safeguards for its employees the December 2007 tragedy may have been averted.
Mr Gray said the firm had never sought to "evade its responsibilites".
The advocate also said Svitzer was a reputable employer which had taken its responsibilities for its workers extremely seriously.
Svitzer Marine admitted "failing to ensure, as far as reasonably practicable, the health, safety and welfare at work" of the crew.
Judge Lord Turnbull adjourned sentencing until November 13 at the High Court in Edinburgh.
In a separate case, harbour authority Clydeport Operations Limited also faced a similar charge in connection with the Flying Phantom incident.
The case against Clydeport was adjourned until a further hearing due to take place over two days in December, also at the High Court in Edinburgh. An earlier Marine Accident Investigation Branch (MAIB) inquiry found that in the incident the boat's towing winch had not released quickly enough, which meant it was capsized by the vessel it was pulling.
The report also highlighted failings in procedure to ensure the tug operated safely in foggy weather.
A Crown Office spokesman said it would be inappropriate to comment while proceedings were ongoing.
He added: "No decision regarding the holding of an FAI will be taken until the criminal proceedings are concluded."