His comments come after defence giant BAE Systems announced that 1,775 jobs will go across the UK.
Shipbuilding will end at Portsmouth in the second half of next year and hundreds of jobs will be lost in Scotland at the Govan and Scotstoun yards in Glasgow, as well as at Rosyth in Fife.
But work on the new Type 26 vessels is earmarked for the Glasgow yards, giving workers there a vital lifeline.
UK Government ministers have already hinted that this work could go elsewhere if people in Scotland vote Yes to independence next September, though Scotland's Deputy First Minister Nicola Sturgeon has insisted Clyde shipyards could still build the ships. Lord Reid said that UK warships would not be built north of the border if Scotland left the UK.
He said: "The wider lesson from the last few days is that the only way to secure the future of Scotland's shipyards is to remain in the UK. This is not a matter of political opinion, it is a matter of fact.
"It is a fact that since the Second World War, no UK Government of any political stripe has ever commissioned the building of a warship in a foreign country. It is a fact that for security, as well as economic and political, reasons we build these ships here at home in the UK."
He added: "In short, we don't build warships abroad now - and what's left of the UK wouldn't do so if Scotland separated."
BAE said there will be 835 redundancies in Glasgow, Rosyth and Filton, near Bristol, and the remaining 940 in Portsmouth.More detail about the job losses is expected to emerge from talks between the company and unions early this week.
The war of words between Ms Sturgeon and Scottish Secretary Alistair Carmichael escalated as he called on her to admit she is wrong on her assertion that an independent Scotland could still build UK warships.
He said: "Nicola Sturgeon is looking pretty isolated on this. The best thing she could do is admit she is wrong. Is she really saying that everyone else is wrong and she is right? Is she telling us that the people who build the warships and the people who place the contracts know less about this than she does?"
Ms Sturgeon rebuffed suggestions that Scottish yards would not get the work if the country leaves the UK.
She said: "The decision to close Portsmouth will leave the Clyde as the only place on these shores with the capacity to build naval surface ships -- and that decision is testament to the world-class skills of the workers there."