The Government has been criticised for ignoring the bid, which would have helped bring jobs to the Clyde.
Defence Secretary Phil Hammond revealed last week that the preferred bidder for four military support vessels was Korean firm Daewoo, meaning no work for Scottish yards.
The Ministry of Defence said there was no bid from UK firms for the £450million deal, but 20% of the work would go to a design facility in Bath.
However, it has emerged that a rival bid from Italian company Fincantieri would have delivered 35% of the work to UK yards, including a deal with BAE, which was being discussed.
Shadow defence secretary Jim Murphy said: "People in Glasgow will feel jobs are being sold down the river.
"Rejection of this bid will mean work that would otherwise have gone to UK shipyards, including potentially the Govan shipyards, will now go overseas."
The four 200-metre Military Afloat Reach and Sustainability vessels known as MARS will cost the MoD £452m.
The ships will provide fuel and supplies to other ships at sea.
Mr Murphy is angry that the order, rather than securing jobs on the Clyde, will see tax payers' money going to workers in Korea.
He has written to Mr Hammond asking for clarification of when he was aware of the rival bid, and whether the Government has assessed the impact the deal will have on the loss of skills in the UK shipbuilding industry.
Jim Moohan, chairman of the Confederation of Shipbuilding and Engineering Unions, said: "The MARS Project would have ensured job security would have continued.
"The new tankers are worth £500m, clearly vital work that should remain within the UK.
"This has jeopardised the long-term security of UK shipbuilding.
"It is an Exocet to UK shipbuilding."
However, the MoD said the South Korean bid offered the best value for money.
Peter Luff, minister for defence equipment said: "This project will inject up to £150m into UK industry, and support and maintenance will also be carried out in the UK. The Government remains committed to building complex warships in UK shipyards."